If I was going to guess, which is about all I can do without looking at the programming, I would say that in Night mode incoming calls are sent to a Phantom Extension. This phantom extension probably exists on the phones that ring during the night mode.

Are the 2 phones that ring at night have the same number of buttons? What may be happening is that the phone that can not retrieve the call on hold has the phantom extension on a button that does not exists on their physical phone. If the phantom was on the 2nd row of a 20 button phone, but the desk only has a 10 button phone, then they could answer the call but could not see the call on hold.

You could put the system into night mode and look at the working phone to see which button flashes don an incoming call.