buncha things to do.
1. Totally abandon Caucasus, strip it except for the industrial complex. This only if you have UK and US bombers nearby to strat bomb, AND if there aren’t any targets for the Allied bombers to hit - like German navy. This is rare.
2. Stick a few infantry in there, move AA gun out. Only good if Germany’s air is some distance away. If Germany DOES take the Caucasus with infantry/fighters, its fighters are forced to land on the eastern front, giving the UK and US navies some breathing room in the Atlantic. Only to be used if you know EXACTLY what you are doing. Of course, if Germany attacks with infantry/artillery or tanks, you can kill Germany’s forward placed mobilized units, which ends well for Russia.
3. Stick a few infantry and the AA gun in. Pretty much as above, but this is if Germany has better placed fighters. Now, though, if Germany attacks, it risks losing its precious fighters. Russia should not risk fighters in the counterattack; Russian fighters hit the Ukraine, and the bulk of Russian forces from Moscow and West Russia counterattack into Caucasus. This leaves the Germans free to go north into Karelia/Archangel, but that route can be cut off in turn by UK transports.
Things to watch out for:
A. Japanese fighters landing in Caucasus.
Those are just a few options. 2 and 3 go together (the “Kar/Arch” route risk applies to (2) as well as (3)). But GENERALLY, that is the Caucasus. Basically, I think Russia can afford to let Germany capture Caucasus early (depending on the Jap fighter situation); but Russia MUST be able to counterattack without fear of German retaliation. That usually means that Russia cannot afford to let Germany capture Caucasus on G4 or G5 because by that point, there will be a big stack of German infantry in Ukraine or Belorussia, or even Karelia - if Russia counters a Caucasus capture, Germany can re-take the Caucasus from Ukraine and kill the heart of the Russian offense; or move into West Russia from Belorussia and force the Russians to attack German infantry and Japanese fighters, or head east from Karelia and take Archangel, which means that Russia has to pull back from Caucasus, and leaving Russia with no counterthreat.