I'm not familiar with how FEDSIG power supplies work but idle capacitors can degrade over time.
You can google "capacitor reforming" to learn more.
It could be that if the caps are in a degraded state, that FEDSIG designed in some protection strategy to self-turn off when it recognizes the caps not performing as expected.
If this is true, then I'd expect if you keep doing what you're doing (apply power, watch it flash a few times, remove power, wait a few second, repeat), that you'd start to see more flashes before it stops working. This would suggest you're succeeding in reforming the caps.
One thing to keep an eye on is the temperature of the caps. If they get too warm too quickly, that's bad. Let them cool down then re-start the process.
Again, I'm not familiar with FEDSIG stuff but I would expect to see some improvement in just a few minutes.
Off course, be very careful around the power supply -- it is a high-voltage device.