We don't have an explicit, smoking gun that proves with absolute certainty, but we do have a general pattern of behavior and inferences that certainly support the contention, and plenty of reputable authors who will fall on that side of the debate. If you don't mind me doing so, I'll copy an old response I wrote which looks at the Soviet-Polish relationship of the period:

The Polish Home Army (Armia Krajowa - AK) was a formidable fighting force in 1944, and while they were principally opposed to the Nazi occupiers of Poland, their relationship with the Soviet Union was at best at cautious one for obvious reasons. The Soviets, after all, had invaded Poland too in 1939! There were clashes (and cooperation) between the Home Army (which was aligned more with the Western Allies, and connected to the government-in-exile in London) and Communist backed groups, but the Communist groups were tiny in comparison to the nearly half-million member force that the Home Army had raised!

With the Soviets advancing from the east into Poland in 1944 though, cooperation became more common, at least on the face of it. When the Soviets were apparently within striking distance of Warsaw, the Home Army decided to rise up and openly contest German occupation of the city. A major reason for this was that they wanted to liberate it themselves, not be liberated by the Soviets. However, they believed that while they were going to be taking the initiative, the Soviets would at least show up and provide backup soon. In this, they were sorely mistaken.

Like I said, the Soviets may have been playing nice to the Pole's faces at that time, but their underlying opinion had changed little. The Soviets viewed the AK as a direct threat to their goal of hegemony over Poland in the post-war era. For a little background to better understand the underlying situation, we can look back to before the USSR even invaded Poland, and to the purges of the 1930s. Ethnic Poles were some of the worst treated during the purges, and seen as enemies of the state. 143,810 were arrested, and 111,091 executed. According to Beevor's "Second World War", this rate was 40 times higher than the average.

Following the invasion of 1939 and prior to being pushed out in 1941, the Soviets quickly moved to reshape eastern Poland into a pliant vassal. At Katyn Forest the Soviet NKVD executed roughly 8,000 officer POWs and about as many other notable persons (Not a historical source, but I would recommend watching the Polish film Katyn if you are interested in that bit of history). Aside from the executions, some 110,000 people were arrested to be sent mostly to labor camps. These were mostly anyone seen as a possible enemy of the Soviet mindset - doctors, lawyers, petite bourgeoisie, nationalists in general, etc.

It is also worth noting, of course, that the Soviets totally denied doing any of this. After Barbarossa, Katyn Forest came under German control, and they uncovered the mass grave. Of course, they quickly publicized their discovery and brought in neutral observers from the Red Cross to verify that it had occurred during the period of Soviet Occupation. The Soviets denied it and claimed the Germans were trying to smear them, and the Western Allies, not wanting to provoke a major ally (USSR) to appease a minor one (Poland), just kind of avoided the issue, and nodded their heads at the Soviets and told the Polish government-in-exile to not harp on the matter. Following the end of the war, no further investigation really happened and the massacre was casually mentioned at Nuremberg but not as a major charge, and it wasn't until the 1990s that Soviet archives revealed the truth, and Russia admitted what had happened and apologized. An two-part article I have from the 1970s offers an interesting glimpse into the matter - it has a Western writer who kind of implies the Soviets did it, but really just lays out the evidence and tells you to make up your own mind; and then a Soviet author write the counter-point article with the disturbing conclusion that, "Thus was unmasked the provocative act of the Nazis, thus was established with complete clarity the fact of the monstrous killing by the Nazi authorities of Polish prisoners of war at Katyn Wood."

I'm digressing though, the point is, that the Soviets were incredibly harsh towards Poland, not just in mass executions and arrests, but also deporting 140,000 civilians in their occupation region far east over the Urals. The aim of this strategy was to gut Poland of any meaningful resistance to Soviet control. And while they were soon after kicked out by Germany, that didn't really change their outlook.

So now we return to 1944, with the Soviets a hop, skip, and a jump away from Warsaw, and the AK rising up in force to take the city. Except as you probably know, the uprising failed, and Warsaw was utterly flattened, with hundreds of thousands of Poles - both fighters and civilians - dead. The Soviets barely lifted a finger in support. The big question is "WHY!?"

There are two schools of thought, which in my opinion are not necessarily mutually exclusive. The standard explanation from the Soviet side is that they had been advancing hard, and were spread out and exhausted. The men needed to rest before another major operation could begin, and forces needed to be re-provisioned and reinforced (you'll find this argument in Zhukov's memoirs, along with almost any other Soviet history). Plus, the AK didn't coordinate with the Soviets very well, and if they had, could have timed the uprising better. So basically, the Soviet view puts the blame on the Poles for losing, and absolves themselves of responsibility by saying they couldn't have helped no matter how much they wanted to. And there is some merit to this position. The uprising was on the tail end of Operation Bagration, so it is certainly true the Soviet had been going balls-to-the-wall earlier on.

But nevertheless, it isn't an explanation that sits well. The flipside argument is that the Soviets purposefully let the uprising fail. The reasons for this should be obvious I think, since it would (and did) severely weaken the AK, reducing their ability to resist the Soviets following "liberation" of Poland. And there is plenty of evidence for this. Stalin's personal statements about the rising were pointedly anti-Pole, and the Western Allies were denied the right to use Soviet airspace in supply-drops that they made, which meant planes had to make long round-trip flights as opposed to one-way hops finishing in Soviet territory.

The one thing that we lack though is the explicit order from Stalin that states not to advance on Warsaw until the AK is defeated. There is a very clear pattern of anti-Polish behavior and rhetoric that allows us to infer this motivation, but that's the best we can do. In the end, it isn't really as if the two positions are mutually exclusive though. Just because the Soviet Armies were spent at the time doesn't mean that Stalin wasn't also ecstatic at the prospect of the AK destroying itself of course, and even more than that, just because the Armies had been in heavy fighting for the past few months doesn't mean that, if necessary, they couldn't have made that extra push had the command been more inclined.

So anyways, from August 1st, 1944 through the next two months, the Polish Home Army fought valiantly, and in vain, to liberate Warsaw, and failed. The failure was a devastating blow. Not only was the city in ruins now, but some of the best fighters in the AK now lay dead or in German hands, and hundreds of thousands of civilians (those who weren't killed in the fighting of course) now were expelled from the city, many going to concentration and extermination camps. It wasn't until January, 1945 that the Soviets finally reached Warsaw, and they ordered the Home Army disbanded, which it did rather than resist. It was clear that the Western Allies were not going to press the issue for a free and non-Soviet dominated Poland, which certainly disheartened many. Not all of them laid down their arms, and those who not resisted the Soviets were known as "Cursed soldiers", fighting in a number of different resistance groups, but their numbers were never large enough to seriously affect Soviet control, and most had been killed, captured, or simply gave up and slunk back to civilian life by the early 1950s.

It is also worth noting that the Soviets were quite merciless to members of the AK. Thousands upon thousands were arrested in the aftermath of the war, simply for their previous membership. Many were accused of collaboration with the Nazis (because they had fought the Soviets... even though they were also fighting the Germans at the same time). The leadership who had not fled west, or at least into the woods, was mostly executed after showtrials, and thousands ended up in the gulag.

TL;DR

So to sum up the answer to your question, the Poles failed to effectively resist the Soviets because the Soviets, since the 1930s, had put in place a very effective campaign of persecution, pointedly designed to eliminate the most likely forces of resistance against their control of Poland. During the war, the Soviets did as little as possible to assist the Polish resistance, further ensuring it was weakened, and with the abandonment of the London government-in-exile by the Western Allies, any chance of outside support against Soviet hegemony over Poland was over.

The topic was covered well by Glantz and House's When Titans Clashed which is a thorough study of the war from the Soviet perspective. Some brief background, then their opinion (which I agree with).

Following the 1944 summer offensives along the entire Eastern Front (including the massive "Bagration" Offensive which started east of Minsk) and the huge armored and mobile force exploitation which followed finally dislodged all German and Axis forces from Soviet 1939 territory, the drained and exhausted Red Army followed its standard doctrine and closed on major river lines and seized bridgeheads on the western bank for future operations after rest/refit/resupply/reinforcement. The river at the northern end of the front following this operation happened to be the Vistula, and the Red Army had advanced over 550km from their start point to that river in two months of heavy fighting.

This series of Soviet offensives took place at the same time as the Allied breakout in Normandy which culminated in a German Army (7th) being surrounded at Falaise and crushed, while in the east Army Group Center alone lost about 400,000 casualties and 30 divisions permanently. It was the largest single battlefield loss the German Army had ever suffered, and the Red Army looked poised to steamroll all before it. To say that these were crushing blows is an understatement.

This is the moment, while the Western Allies were seriously organizing emergency plans to drop airborne divisions on Berlin in the case of a German political collapse and a conspiracy of German Generals were attempting to assassinate Hitler, that the Polish Home Army chose to rebel against the German occupation authority. As we know, the Polish Home Army was loyal to the Government in Exile (GIE) in London, and the Soviet Union had hastily recognized a small cabal of Polish communists calling themselves The Polish Committee of National Liberation which appeared to be a rival Soviet-backed government as soon as they set foot on Polish soil. So the Home Army thought it would be politically preferable to liberate themselves, and then probably publicly declare their support for the GIE rather than be liberated by the Soviets and potentially have a new government imposed on them by their erstwhile liberators. Obviously everyone, and the Home Army in particular, underestimated the brutal fanaticism of the last year of Nazi rule, or the nearly unbelievable lengths Nazi police and SS forces would go to in order to suppress the Polish uprising (just google Task Force Dirlewanger if you have a tough stomach and want to know more about the atrocities).

Now, the Soviets had a bridgehead about 10km from the city center and this is where the controversy comes in. Did the Soviets purposely deny aid the the Polish Home Army? As a premeditated policy, no. The Soviet forces across the river were at the end of a shaky logistical tether, operating outside Soviet territory for the first time, and lacked any sort of organization for supporting the Polish Forces either directly or indirectly (i.e. artillery or air strikes on German positions). Since the Red Army had had no prior notice of the uprising, they did nothing to prepare for it. Further, the Red Army High Command was probably looking at 'big picture' strategy rather than the plight of the Home Army, not entirely unlike the Western Allies choosing not to bomb the rail yards leading to Auschwitz: the best way to stop Nazi atrocity once and for all was to win the war as quickly as possible by defeating the German Army in the field.

The Soviet leadership also blundered by refusing to let the Western Allies use Soviet controlled airstrips to drop supplies and weapons to the Poles (the wildly insular Soviets refused pretty much all of these types of requests throughout the war: the pilots involved in the Doolittle raid that landed near Vladivostok in 1942 were interred for a year and had their plains confiscated) which made it look like even more of a deliberate policy to not aid the Home Army. So, in the end the Soviets handled the PR of this event very poorly, but as far as I have ever read there haven't been any mentions of deliberately withholding support for the uprising as it was happening, and there is evidence that the timetables for the next Soviet offensive was sped up to liberate Warsaw more quickly after the international backlash.

However, it must absolutely be noted that as shrewd a political operator as Josef Stalin not noting the extreme convenience of the Germans killing the Poles who were politically opposed to his intentions in Eastern Europe, and backed by a legitimate government recognized by his allies, is a highly unlikely scenario. Although it is unlikely to have been deliberate, the Soviets were happy to accept the realpolitik payoff.

May I up the ante with an additional question? Does any evidence exist regarding the timing of the uprising insofar as trying to hasten an armistice before being overrun by the soviets?