Their initial stocks weren't at the level they should have been no, again that was poor preparation. But ultimately the logistics failed because, as Darkrenown said, they simply could not get supplies out to their troops at a fast enough pace. They had plenty of depots and reserves, but no way to get the supplies from the depots and reserves to the troops. Key issues were transportation.
First the majority of the rails were of a different gauge then those used in Europe, so after the Germans finally got wise and started move along the rails, (Initially they moved along the roads which kept the rails in Soivet hands for the most part) they were forced to replace the tracks so they could be used by them, and this proved incredibly difficult and time consuming. Since rails were out of the question they had to rely on roads, the problem here is the trucks were designed for use in Western Europe, out on the broken roads of Russia they were useless.
Some telling stats stats to give you an idea, on the first 19 days of operations 25% of their trucks had broken down, 17% beyond repair. For Army Group North, one of the depots that operated along one of the few functioning rail lines was supposed to receive and unload supplies every 3 hours, in reality it took 80-100 hours. The Luftwaffe in Eastern Europe were functioning at a 30% operating rate due to their inability to receive supplies at a steady rate and a chunk of that 30% was used to fly fuel out to the panzer divisions. By the end of July units ammunition stocks averaged below 50% and this dropped to 20% in the first week of August. Because of that limited ability to deliver supplies they had to prioritize. Ammo was given primary with fuel getting a slight cut. Food, clothing, repair parts, guns, ect, were almost completely halted. As a result only 47% of the mechanized units in the Panzer divisions were operational by August's end, most forced to sit on the battle field needing simple repairs to become operational, the troops were forced to pillage, and they lacked proper gear for the coming fall/winter weather shift.
Germany had plenty of supplies and reserves set up, but due to poor infrastructure and terrible planning (And several other issues I listed above) they could not keep supplies flowing to their troops at a reliable rate. And these numbers are just the first couple of months that led to the August Pause which was the grinding halt on the Panzer divisions. We're not even into the fall and winter time when weather impacted the logistics and slowed it down at an even greater rate.
I just don't understand why people are finding it so hard to believe that units ran out of supplies and were forced to halt for an extended period of time. It happened countless times during Barbarossa, Japanese troops were fighting starved and bullet less on the various islands in the Pacific. The U.S., by far the most logistically capable nation in the war, had frequent supply issues in North Africa and Europe. Hell there were a couple Panzer divisions that were forced to halt in France and the low countries for a day or two due to low fuel. Logistics was incredibly difficult to plan and even harder to actually do. Does it happen more frequently in HoI 3 then it did in real life, yes. Is it at a much higher rate, not really no. Unfortunately there are system limitations that prevent them from using ideal models and this lends to that higher ratio. But why people act as if it didn't happen and try to ignore the fact it was incredibly difficult and at times impossible to get supplies from their depots, reserves, caches, sources, ect. to their troops on the front line is beyond me.