Three things:

#1) For any game, heat will cause fuses to blow (they are mostly thermal devices) so loose connections, corrosion, etc. on the fuse holder which could cause spot heating.

#2) For E/M games with linear power supplies, high line voltage will cause higher current draw

#3) For more recent games with switched-mode power supplies, low line voltage will cause higher current draw. Voltage distortion / waveform collapse related to too many nonlinear (not sinusoidal current) loads on the circuit might also be an issue.

Because you seem to be having problems across multiple games, check your line voltage. Could be undersized branch conductors, long run length, loose connections on outlets, etc.

Electrical power quality is (one of my) day jobs; I imagine folks with a lot of games plugged in might run into problems overloading a circuit now and then.