I've narrowed it down (i think) to either a coil or thermostat. Any way to tell which it is? Is this a normal problem?

StephanieM

Have you tested to see if the element is getting voltage?

element is getting voltage

If the heater is getting constant voltage, it doesn't sound like the thermostat.
OHM out the element, should be between 9-12 OHMS. If it's O/L, replace the heater.

Be aware, if the spa is on a 20 amp dedicated 120 volt circuit, it only gains approx ~2 degrees (F) an hour, assuming you have a quality spa cover. Uncovered, it won't heat.