A Russian military expert has argued that Russia should completely scrap its Caspian Sea Flotilla, saying there is no practical purpose for the military presence there and that Russia's thinly spread resources would be better used elsewhere. Mihkeil Barabanov, editor of the Moscow Defense Brief, argues that Russia needs to rethink its entire naval structure, in an article in the Journal of Slavic Military Studies (behind a paywall). And that means getting rid of the Caspian Fleet, he writes:
At present, the existence of the Caspian Flotilla does not make any practical sense because of the weakness of the naval forces of all the other Caspian states and the absence of any real missions with respect to the combat use of the flotilla. If necessary, Russia will be capable of transferring the necessary forces and means to the Caspian from all three fleets in the European part of the country or calling on border forces and aviation.
Russia can transport ships of a certain size from the Black Sea via the Volga-Don canal, and Barabanov recommends keeping the Black Sea Fleet. His logic is, Russia is most likely to fight conflicts with the U.S. or its Western partners, and/or with anti-Russian governments in former Soviet states. Those are conceivable in the Black Sea (with Georgia, of course, but also possibly Ukraine) but not really the Caspian.
I asked Dmitry Gorenburg about that idea for the Caspian, and he disagrees with Barabanov:
I don't think the Caspian Flotilla is going to be critical for Russian security in a traditional sense. No one is going to attack Russia via the Caspian Sea. However, it can play an important role in dealing with transnational security threats. In the Caspian, this includes smuggling of weapons and narcotics, as well as the possibility of sabotage of offshore energy infrastructure. If the flotilla were to be focused on dealing with those types of threats, it could make a significant positive contribution to Caspian security.
The only traditional military role I can see the flotilla playing is in assisting Azerbaijan in the event of a conflict between it and Iran over the disputed maritime border. But that scenario seems relatively unlikely to come to pass.
Russia has announced plans to strengthen its Caspian Sea Flotilla, but the plans seem a somewhat lower priority than other naval forces. So in a situation of limited resources, and if Barabanov's way of thinking is well represented in Russian naval circles, then the Flotilla could continue to stagnate as it has for the last 20 years.