I've moved 4 modems from one account (coheat) to another (PinnacleTeltonika) and I am encountering the same behaviour.
Modems that were connected perfectly under the "coheat" account (so must have all the correct settings) do not connect to the "PinnacleTeltonika" account. This is true even after the modem reboots. (I have an auto reboot set each day)
Only by going to the modem in person, factory resetting the modem, and upgrading the firmware (to V.06.00.00 or higher) will these modems then connect to RMS.
I think this is a bug somewhere.
I will try "moving" a modem by first upgrading the firmware (to V.06.00.00 or higher) AND changing the RMS port settings, then moving the modem to another account.