I haven't checked for a long time, but previously when I looked in the save file Influence is listed twice under the empire's resources. Not sure of its still an issue.

What i noticed was that it didnt matter if I had the mod on or not when reloading a save. the influence value didnt change. so it might be something to do with how the influence value gets saved/stored in the save file.

That is very odd, though I did recently experience the same thing myself in my current game. Had 8 influence when I'd loaded in, despite knowing for certain that I was in the low thousands. I'm confident enough in saying that it only happens when you load a save, though at this point I have no idea why it's happening.
Looking back at the code of the mod, I haven't changed anything other than the maximum for influence, so that makes me think that it's a bug with the game itself. As such, I don't know how to fix it, or if it even can be fixed on my end.

had the same issue. always wondered why my influence was so low. apparently it deletes some of your influence either when you safe or when you reload. had a run where i was supposed to have 212 influence (4 years 6 months into the game x4 income 216, +100 starting influence and - 2 starbases built -104) but when i reloaded the safe i had 6 influence.

@comdra6
Really? I'll have to take a look at that, since that most definitely doesn't sound fun. Thanks for the notification.

This has a bug where Stellaris will force the influence counter to return to something less than 1,000 upon loading a save. If you try to restore it through the console, it will revert to <1,000 upon reload. Eventually it will result in a hidden negative value that will trip a "critically low resource" regardless if the value it positive on your screen.

at last finally someone see the sense in this!