^^ Exactly.
Yes, *technically*, repeatedly cycling power is to be avoided as miners are designed to be ran 24x7x365 at a fairly high chip temp. Shutting them off long enough for them to cool down to ambient temp and then restarting & getting back to operating temps DOES add stress to solder joints each time it happens. We are talking chip temps that are around 20-30 deg C above ambient. With that kind of temp swing materials expand & contract causing the stress and yes, the damage does add up when it happens a lot.
That said, shutting down to troubleshoot is not an issue. Fixing the problem is much more important.
I will add that if the controller allows you to stop mining for doing a controlled cool down with the fans running (Avalons and the ePIC controller board do) then yes, that is better than just killing power because there is no chip temp spike.
Oh, and all Avalons' since the A10 do have a power on-off switch on their PSU but it just kills the power - no controlled cool down when using the switch.