Nothing posted so far covers the obvious, so here it is:
1) Have you tried using a different bass?
2) Have you tried using a different instrument cable?
3) Are the basses you're trying active, and do they have known good batteries?
4) If it's none of those, then I would check the input jack on the amp and make sure it's clean. I've heard of equally weird problems that were just from dirt in the input jack.
Yeah we've tried all of that already, aside from checking for dirt (which I'll do now) but at this stage I'm 99% convinced the problem has to be the amp unless all of my gear has failed simultaneously.