One of two things: Either there is a fault somewhere between the alternator terminals and the DC aircraft electrical system and busses or you are placing a greater load on the A/C electrical system than the alternator can handle.
For electrical issues, I would have the airplane inspected by a qualified mechanic and check the alternator, the DC rectifier as well as all of the connections between these systems and the electrical busses. For load issues, take the airplane out on the ramp where you can safely do a run-up and follow the run-up checklist for your airplane. With the engine running at between 1700-1800 RPM, switch on all of your electrical components - all of the lights, the pitot heat, the boost pump, the 12V lighter, etc and monitor the ammeter to verify it remains positive throughout the runup. If it starts drawing current off of the battery, you may need to have the alternator inspected and replaced.