Old 9v battery - Strange Behavior
Voltage drop will differ depending on which device you are using, but is safe to say that it should not be dropping that far with a low power garage door opener. A .1 V drop is much more realistic and intuitive. To answer your question it is not very characteristic of batteries near the end of their life to have a higher unloaded voltage reading than before they were initially used; and although the fact that it is used may play some effect in swinging the voltage lower than it might normally drop, it should still not result in a 6 volt drop (or anywhere near that). I think it is okay to assume a defective battery.