1990 Heater: Trane XL80 w\ original Trane A\C - heat pump
1990 Thermostat: Trane Weathertron

Last year, problem began occurring whereby our heater will not lite unless we switch to 'emergency heat'.
Then, the heater unit will ignite and the heat pump eventually shuts off, making our system operate like a traditional (expensive) heating system without any heat pump assistance.

The A\C unit works fine in the summer.

The heater and heat pump used to work together automatically, now they will only work manually.

What could have broken?

What you describe is the way they are suppose to work, you cannot run the heat pump and the gas furnace at the same time, only the furnace fan should operate when the heat pump is working. When the heat pump can no longer keep up with the demand then the heat pump shuts down and the furnace takes over or when the out door thermostat makes this transicion. Good luck, Mike

When the heat pump can no longer keep up with the demand then the heat pump shuts down and the furnace takes over or when the out door thermostat makes this transicion. Good luck, Mike

Shouldn't this process occur automatically?

We didn't used to wake up to a 60 degree house and have to manually switch to 'emergency heat'.

So, my question is, what's BROKE?

Yes this should be automatic, you may have a bad outdoor thermostat.

I agree with acetc. The out door thermostat or sensor is what tells it to use gas furnace or heat pump. When you switch to emergency heat at the t-stat you bypass the outdoor stat.