Move the GFCI
GFCIs have sensitive electronic components, as you found out the hard way. A regular outlet does not. If you can move the GFCI protection to an indoor location and then replace this with a regular receptacle, that would solve the problem permanently while still protecting against ground faults. Two options:
Earlier in the chain. If there are other receptacles as part of this circuit before this outlet (e.g., possibly the bathroom that is on the same circuit), replace one of those with a GFCI receptacle. Just make sure that you use line vs. load correctly so that this receptacle is protected (on load screws).
At the breaker. If you have sufficient space in your panel, replace the regular breaker with a GFCI breaker. That will protect the entire circuit.
As already noted, you should have an in-use cover on any outside outlet. This will help prevent nuisance trips due to moisture, though it is not a 100% cure-all and therefore moving the GFCI inside makes sense in any case.
Based on additional comments: It appears that the bathroom receptacle already has GFCI. If that is the case then (a) no need for a GFCI breaker and (b) need to check whether the outdoor receptacle (and any others in the circuit) is pigtailed to share the line connection or is actually using load. If the outdoor receptacle connects via load then it is already protected. Open up the bathroom receptacle box. If there are wires on both line and load, then wire up an ordinary receptacle in the outdoor location. Make sure it works. Then press the TEST button in the bathroom.
If the outdoor receptacle responds to the bathroom TEST button (i.e., when TEST is pressed, both bathroom & outdoor have no power, when RESET is pressed both bathroom & outdoor have power again) then you do not need a GFCI on the outdoor receptacle because it is already protected in the bathroom. Only one is needed but keep in mind that it protects "outward" - i.e., if the sequence is breaker->bathroom->outdoor then a GFCI breaker or a bathroom GFCI will protect bathroom and outdoor, but a GFCI outdoor will NOT protect the bathroom (though as we've discussed, you shouldn't put the GFCI outdoors anyway).