Late Game FPS Drops

So I admittedly don't have a great computer, that alone may be the issue, but I am looking for some sort of ideas to fix this issue, as I really want to play, but at the moment I can't unless the game is over by 25 minutes. For the vast majority of the game, I get around 50-60 fps, which is more than enough to play well, however, past the 20-25 minute mark, things start to slow down noticeably. During team fights I'll get almost to single digits, and float around 20 or so when i'm not near any other champs/minions. If the game goes longer than 40 i gets pretty much stuck at 8-10 permanently, which as I'm sure you could imagine, makes me damn near useless. I have all the graphics settings moved to their very lowest/turned off. This issue just started a month or so ago, as before this I used to get 50-60 through the whole game, and it's frustrating as I want to play ranked, but I don't, cuz I don't want to cost my team the game because I am moving too slow to see what's going on. Any and all help would be greatly appreciated