I'm having a similar problem...
I have a board with a regulator that takes a 9V supply from a mains adaptor down to 5V, and powers a Bela Mini from that, which works fine. But I when I try to bypass this regulator and power the Bela Mini directly from a bench top power supply (for testing purposes), nothing.
I've tried powering the Bela Mini on both the SYS_VIN (P1.1) and USB_VIN (P 1.7) pins, but no luck. I've got the bench top supply set to 5V, but when I turn the current dial the current reading stays at 0A...
I'm probably missing something obvious, but any help much appreciated!
PS - there doesn't seem to be anything wrong with the bench top supply, because everything works fine if I put that in front of the 5V regulator on the PCB...
PPS - I tried the test suggested above - powering up by USB, add 5V to SYS_IN and disconnect USB, and it instantly goes off, so definitely not managing to get any current out of the bench top supply