If you want to rule out the automatic backups as a possible cause, try the following, (preferably when the phones are clear to mimic an actual 2am scenario):

a) Test and make sure call forwarding is working; if it's not, reprogram it and check again.

b) Change the system date/time to the 1st day of the next month, 01:58am.

Automatic backups should kick in in two minutes. Wait for it to complete.

c) Test call forwarding again to see if it's broken.

d) Set system time/date to the correct current settings.