I doubt your temp probe has gone bad. It does happen, but those things are rugged, and when they die, they generally read very high or very low, not just a bit off.
Instead of the built in Heater programming, you could pull down the Advanced control type, and enter something like:
Fallback OFF
Set OFF
If Temp < 78.7 Then ON
Defer 001:00 Then ON
If Temp > 78.7 Then OFF
With this kind of programming, the relay in the energy bar will activate quite frequently, as the Apex attempts to keep the temp in this narrow range. These relays are supposed to be good for a million plus activations, so at 100/day, for example, that's a bit more than 27 years. (The Defer command is just for a bit of hysteresis to prevent overly short activations; can be adjusted based on review of subsequent temp input graphs. )