Very likely it's caps then or a faulty joint that's breaking down with heat.
For SMPS I generally focus around the controller IC particularly its VCC storage cap. They seem to drift way outta spec with age and go high ESR and/or low capacitance. Pull and measure is all you can do with these as they never show signs of degradation.
I'm really not an expert, but there are many IC's in this PSU... as stated, it's not an ATX PSU, it's a custom design, that includes an ATX-compliant output, but there are 4 ATX-like connectors (1 ATX 20-pin, 1 22-pin, 1 18-pin, 1 16-pin).
So you're saying that regardless of their aspect, caps can be seriously out-of-specs ?? Not good... is there really no way to locate bad caps in a non-intrusive way ?? This PSU is far from simple and physically quite dense, desoldering all the electrolytics is gonna require a serious amount of time ! Is it possible from the picture above to identify 'more critical/suspect' caps to begin with ?
No, it's more by gut and experience where you go looking first.
Like any circuit some understanding of stress points narrows where to look. Most are well designed with conservative component values and of good quality however the bean counters are always trying to save a few cents therefore reliability suffers especially when crap caps are used.
I've seen PC mainboard caps so furking hot they would burn fingers and other caps so furked they're no longer measuring uF but pF !
Trouble with SMPS one end of them is rectified mains potential which in our case in NZ is ~325VDC which is not to be trifled with
yet the other end of the PCB is often at most 12VDC which I'll happily run fingers over to find hot spots.
What's helped me become comfortable with SMPS is study of the controller IC datasheets and especially their Typical application schematics where you can clearly see each block of what makes them tick...pun intended.
Forget studying the multi-voltage SMPS so much but the basic single output SMPS and each of the bits that need be right for them to be reliable.
Sure you can shotgun many parts and fit new ones but little is learned other than soldering skills however they aren't that hard to diagnose with a DMM and a scope. Cap tests need an ESR meter and I get by with Smart Tweezers for this and most other component tests.
Typical failure points in no particular order for non functional or troublesome SMPS. (not those that have gone BANG !)
HV dropper resistors to the controller IC VCC.
Controller IC VCC cap or flyback diode.
Diodes in general.
Caps, caps and caps.
Did I mention caps ?
Study basic operation principles, it really helps understand these things.
Rasz's comment on the PWRgood rail is something that need not be overlooked as that's another little independant SMPS AFAIK. Trace the PWRgood rail backwards and you'll find where it originates.
it's not very clear to me what you want me to learn from the power-good line ?? Are you trying to detect whether the PSU shutdowns on its own, or on request of the scope ?
Power good line goes down and so does the PSU !
2 channel scope in Single shot mode with a ch on PG and the other on a main LV power rail will confirm if the PG is OK and not the reason it's shutting OFF.