I have this same problem. Sapphire RX VEGA 56 shuts my cMP 5,1 down well before I push it with something like benchmarking software. It lasts 1 minute in some cases and 15-20 in others but it ALWAYS causes a hard shutdown.
Where is the low power mode bios switch? Are you talking about the dual-bios dip-switch? What makes you think one mode is low power? and which switch position is it?
I have an EVGA powerlink and it hasn't helped at all.
Nor has it helped to power it using my NETSTOR external PSU.
Makes me think the 'unbalanced power draw' argument is correct and that AMD should be embarrassed that a world-class GPU has been undermined by shoddy electrical engineering :/
The problem is more complex than appears at first glance. Apple designed MP4,1 around eleven years ago in a world that the power hungrier workstation GPU used around 150W in a very balanced way. Now GPUs use multiples of this and in a very unbalanced way, some using very little PCIe slot power while others use a lot from it. MP4,1/MP5,1 were never designed to have GPUs so power hungry and with so diverse ways to be powered.
AMD got burned with the initial release of Polaris GPUs, they used more power from the PCIe slot than they should and a lot of PC motherboards that were designed without tolerance for overspec power consumption burned the PCIe slots. After that debacle, GPU power plane design changed and hardware engineers in general tried to use less from the PCIe slot and more from the PCIe power connectors, but it's not a rule and we see various degrees of PCIe power balance.
One example that causes frequent problem here, some Dell gaming and workstation GPUs were designed to use more power from the PCIe slot, since the Dell PCs/workstations motherboards were designed to power the GPU mostly from the PCIe slot. These GPUs don't work well with MP5,1, there are dozens of posts about this problem.
Anyway, the problem is that MP4,1 was designed for a different world. We have to thank Apple for how tolerant and resilient the power design proved to be, but eleven years later it shows it's age.
You should check if your NETSTOR external PSU can cope with the VEGA 56, maybe this GPU is defective. Did you tried it with a PC that is capable to power it?