This is a Regency Spa manufactured by National Equipment Mfg. Corp. It is about 13 years old. No brand name on controls, but shows type as SSS HT-12 Convertible. No owner's manual.
The heater works, but cuts off when the water temp reaches just below 80 degrees. The in-spa control is set at 102, but it does not seem to matter what it is set for.
The light on the heater goes on when it is heating/off when it is not, as expected, but the pump motor keeps running whether heating or not if the system is switched to temp control (pump goes on/off normally when using timer control).
Water flow volume looks normal, and filter is clean. Test shows no juice to heater from control panel when it goes off, meaning something in the control panel is shutting it off. I.e., the problem is not the heating element and is not in the black box connected to the heater. Any suggestions?

Sounds likw a thermostat problem. Try temporarily removing the temperature probe ffrom the drywell it is in or location it is in. If the spa continues to heat past where it heats to now, replace the thermostat.

CAUTION- Removing the thermostat probe for too long will allow the spa to continually heat and possibly create scaulding hot water.

is the heat indicator on even after the tub stops heating? If so, could be either that the heater element is bad, and you are heating via the latent heat generated from the pumps, or your spa is loosing heat as fast as it's generated, in which case a new cover, or better insulation would be the fix.