Use of a capacitor to accomodate temporary voltage drop
If things worked before you added this delay board, then the problem is with the delay board.  It's not doing its job properly.  It is probably dropping too much voltage, or being too aggressive about thinking power is going away and shutting down.  Either way, this delay board is not a good fit to your requirements.

If you just bought it, then return it and explain what's wrong.  If you designed it, then show us the schematic so we can fix it.