Random Black Screens Mid Game

H'okay, so.

This is a problem that has happened to me at least every other game consistently, and across multiple computers.

Randomly during a game, my LoL will cut to a non-responsive black screen, and I have no choice but to restart my computer and hopefully get back in game before I've died. Sometimes this problem happens once, sometimes it happens all fragging day. I've tried uninstall/reinstalling, I've checked the temps, I've checked the drivers, I've checked the video card.

Here's the kicker:

I can play hours and hours of Borderlands 2/Burnout: Paradise/Marvel Heroes/and any other game you can think of without this black screen issue happening one time - but I am guaranteed to cut to black at least once during the 15-20 minutes that a simple 3v3 takes.

What is wrong with the LoL client that is causing this to happen, and how can I fix it?