Tuukka was concise and to the point:
As caps age - ESR goes up, capacitance goes down. Due to increased ESR, cap can no longer handle ripple current so the filtered voltage dips resulting in brief periods where voltage into LM323K goes below drop out voltage. Will the reset circuits catch this? Most probably yes. Will users ever catch this brief drop out with a meter? Not a chance.

The bridge rectifier replacement was what had me confused for awhile. Why would so many be going bad. Well my guess is they probably weren't. I think people were pulling old bridges out where the forward voltage drop had increased due to prolonged periods of high ripple current but were still functional. New bridges had lower forward voltage drops which appeared to "fix" the issue...for now.

But as Slochar also says - there are also ther issues such as aging or bad connections. Add in damage to boards caused by ripped out vias and broken traces and things get even worse.

In my opinion, if the problem is unknown then always suspect the cheapest and often the problem parts first --> connectors.

The Kahr module is a good aid to determine if the problem is power supply based but the source of the problem should still be fixed. Continue to use the Kahr module after the problem is fixed? Although I don't see a reason for it if main power supply has been fixed, I also don't see a reason not to use it other than cost. It does have added benefits: It partially offloads the LM323K which is always a good thing. And since it is a switching type power supply - the input current through the big caps and bridge rectifiers is also reduced which is also a good thing.