It's important to understand how it works first:
(1) During standby, the secondary voltages are still low....
Here, the TLP isn't functioning yet....so it can be said that the primary and photocoupler components are all normal....because the standby voltage is normal.
(2) When the power is on, the secondary voltages just rise to normal 5v and 12v. But why does it keep dropping...
This is where the new TLP works...
So, in this case, what needs to be checked is:
The voltage path from Diode D519 and its filter capacitor.
TLP431.
The transistor that should be "off" (Fig. 2) may have a C-E leak. The base voltage at the power-on position should be "0" volts.