What PSU are you using, and which did you try to swap it out with?
You say this issue happens if you start two or four, did you also check 3? (Does it happen in any case you run multiple cards?)
Have you tried starting 4 instances of the mining software, each for a specific card?
I am running 2x EVGA 750G PSU's per MOBO. I have an extra one not being used. I swapped one out at a time to check for other problems.
Yes it also happens with three. it just consistently drops one GPU. Not always the same GPU.