I had the same problem as you. Mine was working with six GPUs. Then it went down to five. Then four.

When I had six running. One would go sick or dead. So I discovered one and removed it from the system. I moved around the PSU power cables to clean it up. Then another GPU would get sick or dead. I isolated that one too. Eventually the whole computer was locking. So I removed that GPU too. I moved these two GPUs to my office PC and ran cgminer. It ran like a champ for days while the mining rig was only running four. I then installed back one of the two by itself and it was fine. So I then proceeded to plug another in. It was crashing. I skipped it and went to the others. They were fine. I went back to the one causing the crash and tried it with another power cable. It worked fine. So I then added the other GPUs and moved off the bad powered rail. Now I got five GPUs working again. I don't think I can get six because of the bad rail. But now I know what the problem is.

I recommend you test each rail on your PSU or use another PSU.

TLDR: Bad rail on power supply cause sick/dead GPUs or lock ups. Moved the power to another rail and it works fine.