Hey how are you
1-If the battery keep dying and the anti theft module keep seeing low voltage condition it will keep triggering the alarm horn.
2- 2 things needs done here ,first a battery drain test and Factory scanner or equivalent to read the anti theft module to retrieve the fault codes and see why is that
it could be a door switch ,hood switch , receiver ,key etc...But in this case since we know the battery dying ,that means some thing is staying on module, short to ground etc.. so that is why you can start with drain test and see which module is doing or circuit , if for example the headlight switch fuse is drawing amps while car off,then we go to that switch and circuit ,
read below for testing for drainage
Battery Drainage Test
2- settings on voltmeter will be on milli amps.
3- go across all the fuses in the car and see which one is reading higher than 0.3 to 0.5 milli amps
4- the fuse drawing more than 0.5 miili amps ,will be the suspected circuit that needs inspection for the drainage.
Get those results and fault codes and post the, back here for me and i can help you further on it
Please let me know
ASE Certified Technician