You will know when the PSU is the problem on your modem/router the signs are very dim light emitting diodes on routers display with connection issues and once you replace the faulty PSU the LED's will become bright again and connection is good again.
Unfortunately whilst this can occur it is not always the case with failing, or misbehaving, power supplies. The most troublesome ones are when the power supply, or more frequently the associated circuits, starts to go out of spec as the components warm up. I've seen many examples where a device will seemingly be working fine when plugged-in, but when actually carrying out it's designed functions, and putting extra load on the circuits, it will not. A couple of examples.
A HG612 would drop sync to the dsl line and not re-connect easily. Visually, when not connected to the dsl line, the device and all the led's would seem fine. It turned out the the power supply was slightly out of spec but it was only noticeable when the dsl line was connected, with extra current being drawn whilst the device was trying to sync. Swapped the psu and all was fine. Then on another HG612 with identical symptoms a replacement psu did not help. It was an intermittent board-level circuit fault and the easiest and quickest thing to do was swap it.
Similarly a Zyxel router (NBG series) was visually working fine but would have problems keeping a connection even though everything was fine for months. The unit was swapped-out under warranty, worked fine for a few months, but it too failed but this time in it's entirety. It turned-out that Zyxel had used capacitors in this and several other models by a company called Teapo that were notorious in failing. On opening it up the Teapo caps were swollen and one had gone bang. It was swapped again under warranty but this time I immediately opened and replaced the Teapo capacitors with Panasonic ones on this and several other units. I was very disappointed with Zyxel for not addressing the real issue of them using sub-standard components during manufacture.
Intermittent issues can be some of the most time consuming and most difficult to track down. I much prefer when something totally fails and you can easily spot the fault. It's a bit like trying to track down those elusive intermittent HR (crackly phone line) faults that disappear just when an engineer turns up to look at it. So much easier if the joint or cable fails totally.
Hopefully Zyxel will promptly swap Spotter's unit under warranty without too much trouble.