One of the problems was that when they pushed on to the Volga, they left some Soviet bridgeheads on the west bank of the Don, which they needed to clean out, but never did, because they were hell bent on capturing Stalingrad. The Red Army used these bridgeheads to build up their forces for the November offensive.
The best the Wehrmacht could have done, IMHO, was just to lay siege to the City, not waste resources in trying to batter it into submission,[I know why they did] and put more into the Caucuses offensive. Here, it might have been possible to reach the Caspian Sea, capture Astrakhan, maybe even Baku for a short while, but the end result would have been the same, and they would have just had to deal with a longer retreat. Because while all this was happening, Stalin would have still been gathering his forces to the NW of Stalingrad, and the offensive would still have happened and probably succeeded.
Now, I always thought it would be an interesting TL to write about if Von Paulus and his generals simply decided to do the decent and honorable thing; gave Hitler the finger, and broke out of Stalingrad anyway, to link up with Manstein, when he got to within 15 miles of the place, thus saving 90% of the troops. No doubt many would die later on, in other battles, [can the Germans win, or at least tie, at Kursk, with all these extra men?] but if Paulus had done that, Hitler would have gone completely apeshit, the senior officers would have all been shot, unless they were somehow able to slip away to Switzerland or Sweden, and untold thousands would not have lost their sons.