There were three, somewhat overlapping, factors that made the Tiger II a somewhat unreliable beast for the Germans.
Firstly, the Panzerkampfwagen Tiger Ausf. B was a rushed and compromised design. The deteriorating war situation added a degree of urgency to creating a successor to the Tiger I and Panther tanks. Despite individual battlefield successes, neither the Panther nor the Tiger I had reversed Germany's reversal of fortunes on the Eastern front. Far from being outmatched, the Soviet tank arm had proved competitive on a qualitative level with their German adversaries and far outstripped them in terms of production. The Heer had conceived of the Tiger as a breakthrough tank for offensives, but the prospects for such an offensive dwindled after the Battle of Kursk.
The larger strategic context of German failure intersected with a preexisting 1942 program to mount the long-barreled 88mm KwK 43 onto a tank chassis. The KwK 43 necessitated a large turret ring, and by extension, a rather large tank. The fact that the Soviets had proved competitive in terms of antitank guns also ensured that the armor scheme for the future German tank also grew. The urgent war needs also ensured that the design for what became the Tiger II had to be at the front soon and in numbers for what the Heer optimistically would be available for the Spring 1944 offensives. Thus the tank design had commonality with the proposed Panther replacement, the Panther II, and other off-the shelf components for its engines and drivetrains. This was a counterproductive decision because these engines and drivetrains were already having problems propelling much lighter tanks. Placing this system in a 75 ton Tiger II was asking for reliability problems. Operational experience and Allied testing bore this out as as Tiger II often broke down after extended travel.
Things would have been bad with these design flaws, but material and labor shortages in the German war economy compounded them. Allied strategic bombing forced the dispersal of German industry, leading some tank components to be subcontracted out to inexperienced manufacturers. The increased reliance upon forced and slave labor likewise led to poor components. Both of these decreased quality control and Speer's rationalization drive encouraged German manufacturers to increase numbers. So a number of German tanks entered into combat with preexisting defects. Ersatz materials and other substitutes added further problems. Poor lubrication oils, fuel, as well as faulty gaskets and seals were commonly reported problems for the newly-former Tiger II groups. Multiple components broke down under field conditions.
These breakdowns were not just the fault of material shortages and design problems. The massive losses in the Panzer arm over 1941-43 led to real problems with replacements. Although there were still a core of veterans within the Heer and Waffen-SS, German tankers were increasingly younger and less-experienced by 1944. Fuel shortages and the need to get replacements to the front led to severe cutbacks in German tank training as the training course went from 16 weeks to 12 weeks in 1943.
There was also a major bottleneck for Tiger/Panther crew and mechanics. The preexisting Panzer training utilized much smaller, less-complicated tanks for training purposes. The large and complex German heavy tanks posed a problem for familiarizing recruits to the specific needs of these machines. The Germans attempted to rectify this by creating special training centers such as one for Tiger crews at Paderborn. But both production shortfalls of Tiger I and IIs as well as the urgent needs of the front meant that the Germans could never meaningfully expand these training courses.
The result was that the Panzer tyros often handled their tanks poorly. In the case of the Tiger II, there were a number of drivers that often gunned the engine or shifted gears to quickly, straining an already-stressed engine. Mechanics and other support staff likewise did not do well under these combat conditions. German Panzer doctrine had never put much stock into recovery and the logistical tail for the Panzers was very thin. Spare parts were not plentiful and recovery vehicles were spare. The Tiger II's immense weight ensured that the only thing that could tow a Tiger II was another Tiger II.
So these human, material, and design shortcomings all reinforced each other throughout the Tiger II's brief sojourn into battle. The result was that while the Tiger II was formidable on paper, its operational readiness was poor and it was something of a paper tiger in reality.
Sources
Forczyk, Robert. Tank Warfare on the Eastern Front: 1943-1945 ; Red Steamroller. Barnsley: Pen and Sword: 2016.
Jentz, Thomas L, and Hilary L. Doyle. Germany's Tiger Tanks: Vk45.02 to Tiger II. Atglen: Schiffer, 1997.