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The fuse is to protect the transformer so everything that is on the low voltage circuit can be a possible problem, more than likely its the contactor in the outdoor unit that is causing it to blow or some pinched low voltage wiring out there.
You say 2 amp fuse typically they are 3 amps or 5 amps, what color is the fuse ?
OK, its not an on-board fuse but it will serve the same purpose. You have something in the circuit that is overloading the transformer. It's more than likely the contactor in the outdoor unit.
250 VA ? Is that a 120 to 24 volt transformer ?
If it truly is 250 VA at 24 volts you could easily put a 5 amp fuse in there.
I think that 2 amp fuse may be on the primary side ? Could you recheck that please.
Probably , its either that or the wires running between the heatpump and the furnace. The contactor is the only thing using the low voltage out at the unit and if you replaced it that should not be the problem. So either wires or transformer. I suppose you could try the transformer. 250 VA is a large transformer for this application. Generally they are 45 to 75 VA.