So it's recalculated on the next turn.
This isn't correct. AFAIK influence is not specifically recalculated on End Turn.
As Willy mentions influence is recalculated by any action that changes your or an AI's influence. Specifically the colonization or invasion of a planet, the building of any starbase or even just adding a module to an existing starbase. I'm not so sure about the building of an influence type building, but perhaps that as well.
The thing is that during most of the game when you hit End Turn it's almost inevitable that at least one AI will perform one of the above actions causing the influence to be recalculated. However as you get into the later game where perhaps you've eliminated all of the AI's except for one and you've also reduced that AI's planets and may even have killed all of his ships, then you'll find that influence is not recalculated after each turn. In fact I've gone many game years where the influence hasn't been recalculated at all.
As jmgarth mentioned, this has been an issue forever. Generally the biggest problem is that you may have parked some ships along with some transports well inside your area of influence only to find that they are the cause of an AI declaring war on you due to a reload.
Also whether it's your influence that is underestimated versus that of the AI's or vice versa is not always very clear.
For example in the Metaverse League each month we play a game with randomly selected settings and victory condition. To earn the most points you need to win in the proscribed manner while all victory conditions are enabled. Additionally there are bonus point for high scores and fast games (in reported game years). Unless the selected victory condition is an Influence win, it's necessary to avoid it.
To accomplish this it's standard to build influence starbases and gift them to an opponent so as not to win prematurely with the incorrect victory type. The problem is that because of this recalculate issue your influence versus that of the AI can vary wildly and the more influence starbases in the game the wider the variation. Also once you've hit the magic 75% influence threshold the 10 week countdown starts. Even if you can cause a recalculate that causes your influence to go below the 75% level you still get credit for a turn at 75%. The next time this occurs you only need 9 turns at 75% etc. until suddenly you're forced to win by influence. This can be very annoying.