A lot of factors played role here, from legal to downright personal, though ultimately it was, perhaps, just a bad luck.

From a legal standpoint, the predecessor of ChRI in USSR was ChIASSR, unlike Georgia or Ukraine it was not a union level republic, but an autonomous republic inside the Russian SFSR. Only union level republics could (or at least did) secede. However, Chechens invoked a USRR law introduced shortly before the fall that allowed autonomous republics (such as ChIASSR) "rise" to the level of a union republic. So the first changed the level of the republic then declared independence from the USSR, since the modern Russian Federation didn't exists at the point (yes, ChRI is older that Russia, de jure). RF that was declared later didn't recognize this move and still proclamed Chechenya as a part of Russia, though unlike everyone else Chechens didn't get to sign the new federation agreement or take a part in any of the following deals inside Russia. The situation was complicated further when the Ingush part of ChIASSR decided that they want to remain with Russia (mostly because Russia owned their historical lands that were not part ChIASSR) and formed their own Republic of Ingushetia.

Geographically, the resulting territory of ChRI was practically and enclave inside Russia with just a few miles of border with Georgia eith only one road. Economically, Chechnya was too integrated in the regional economy to become truly independent: Chechens closing the oil pipe going through the republic would hurt the Russian oil industry, Russians closing the border would ruin the Chechnya's economy.

All of that could have been settled if not for the political and personal interplay that took place between the (now Yeltsin's) Kremlin and the new Chechen government of Djokhar Dudaev. In short, Yeltsin expected Dudaev to play along and be a loyal puppet alongside other leaders in post-Soviet area. Dudaev, on the other hand, was a proud person, a Soviet general of aviation with impeccable record, a Chechen who lost his parents to a Soviet genocide and had to overcome a lot to become the first Chechen general in the Soviet history; he be the last one to play nice with some loud-mouth politicians be they in Grozny or Moscow. So, Kremlin tried to pressure Dudaev into submission delaying the recognition process, Dudaev responded by calling the Yeltsin's government thieves and neo-imperialists trying to rob everyone in post-Soviet area. Kremlin would be fine with Chechnya's independence, it would not be fine with a decorated Soviet general sitting in Grozny and calling them thieves during their disastrous economic reforms - it was just one step from there for some sympathetic generals inside Russia to heed to Dudaev's words and organize a military coup in Russia.

There begins Kremlin's push to replace Dudaev: they collected a pro-Russia mob from old Soviet nomenclatura from Chechnya; began a propaganda campaign to demonize Dudaev's rule and all Chechens by extension; armed and financed his every opponent in Chechnya. Basically, the same scenario that is applied in Ukraine today. This culminated in the assault on Grozny in November 1994, where the so-called pro-Russian opposition featuring Russian tanks with crews tried to take over the city. The Dudaev's forces quickly destroyed the "opposition" and captured the Russian mercenaries. A few weeks later Kremlin went all out and began an full-scale invasion starting the First Russian-Chechen War only to lose it two years later. In the peace agreement that followed, Russia promised to recognize ChRI few years later, but started another war before that. During the war Kremlin had managed to split the Chechens and secure the support from some of the formerly pro-independence nationalists, while the rest grew increasingly religious and radical pushing out the remaining nationalists, in time, turning the whole thing into a low lever insurgency with little support from the people. In 2003 the new pro-Russia government organized a sham referendum to adopt a new constitution for Chechnya that would proclaim it a part of Russia, the same way Crimea joined Russia.

It's a charitable irony, though. From the Russian point of view, twenty-five years ago in Chechnya they had a dangerous break-away republic led by an uncontrollable dictator with a few thousand henchmen (according to their media). Today, however, after two bloody wars that sucked countless Russian lives (not even counting all the money) the situation is the complete opposite: Chechnya is shining beacon of law and democracy led by a renown human rights activist and his altruistic crew. And any Russian questioning any of it finds himself asking for a forgiveness on the internet.