For some unknown reason, the beeps sometimes stop working (after working fine initially)! This happened to my remotes on my 1995 Q45. Here is my old thread on that:
zerothread?id=8400.
As I recall, when I checked with the Infiniti dealer, they said that they had seen it and did not know the cause. Only cure they had was to buy new remotes - for quite a bit of money, of course! This was back a few years ago, and I doubt new ones are still available.
So, older used ones, from eBay or other places, tend to already be in that mode (no beep) already and no known repair!
Z