If the breaker was for the outside unit, then you likely have problems with the compressor or one of the starting components. Unless you have a thorough knowledge of AC systems and how they operate, there is not much you can do without the proper test equipment. Has nothing in particular to do with being female
It could also be a bad breaker causing the issue, although you would need to change the breaker with a new one to see if this was the case. If it is not handling the normal load of a unit starting up and running, then it could very well be the problem. Certainly a $13 breaker is better than a new unit.