After going through about 100 RB751s and doing burn-in tests, we have seen a few go into that weird state of just flashing LEDs after power-up.

For some reason, plugging in a 24Vdc POE seems to clear the issue, and then subsequent powers with the barrel/wall wart power supply work just fine. Go Figure

Any ideas on what causes this?

I've had a bad experience with these units. They hang randomly, I've sent the support files but mikrotik can't find the issue.

If all LED lights flash at the same time, and changing the PSU fixes this issue - you better send the unit for replacement. PSU change is only a temporary fix, the hardware problem is still there, and your wireless will not work at full capacity. RMA is the only solution. Only devices from the very early first production batch could be affected with this issue.