I installed the BMW alarm system myself but had to have the car programmed at the dealer. The first time, the single chirp was not working. It was fixed by going back on the computer and reprogramming.
The system has not had a fault in "chirping" since then. The parts cost them less than $200 and since they were installed by BMW, if they don't want to reprogram that one, tell them you want a new siren. The other two parts are a interior sensor and a tilt sensor in the trunk. It takes all of about 20 minutes to change the siren.
If they change the siren and it still does not consistently chirp once on locking, they obviously programmed it wrong.