Limit automatic phone call total retry times

is there any way to limit the number of callbacks this program makes?

Yes.

If you are using Auto Reminder, the appointment reminder program, please select Appointment > Customize Appointment… from the program main menu, then set Retry time.

If you are using Broadcast By Phone, the autodialer program, please select Broadcast > Broadcast Options… from the program main menu, then set Retry time.

If you are using Voicent Gateway, you can set the retry time parameter when submitting call request.