Well it looks like I spoke too soon. I just went in and turned on my system and began listening. After a few minutes, the monitors cut out again. I have them going through a Coleman Audio LS3 line selector because I use a mono monitor sometimes to check the mix.
When the KRK's cut out, I switched to the mono one, and it was working fine. I would switch back and forth, and the mono was working, while the KRK's were not. I tried to see if the LS3 was defective, but it seems to be fine.
I have an old pair of M-Audio BX5's, so I switched. These seem to be working fine for now (but they don't sound near as good as the KRK's). If the BX5's don't cut out, then I'll know there is something wrong with the KRK's. It's just odd that both KRK's go out pretty much at the same time - and start working again at the same time.