Something should be said about the movements of 1st Panzer Army. It danced around the battlespace better than George Best could around the football pitch. To continue the football analogy, the Soviet side was using zonal defence instead of man marking. So when 1st Panzer Army was nowhere important, no one picked them up. When they were somewhere very important no one was left to pick them up.

1st Panzer Army surrounded Rostov on turn 54, got to the Black Sea coast at Novorossiysk on turn 56 and the gates of Grozny on turn 57 before turning north and crossing the Volga east of Stalingrad on turn 59. By turn 65 it had crossed the Volga again north of Saratov.
I know the feeling was units could not have been afforded for the defence of the Caucasus - but is there a question of could you afford not to? A few units at Krasnodar to slow the Panzer army down was less than the units needed to stop them at Saratov.
(For those who do not know George Best this will enlighten you https://www.youtube.com/watch?v=dbVatiHiQrc you can also similarly use Eric Cantona or Zinedine Zidane)