I do not know the ages of the battery or the alternator but I know that the battery has not had much use and was originally used on a Landcruiser so it is a high spec version. Never had any power problems at all.
I have tried all your (basic) answers but the connections are completely clean, could eat your dinner off them, and no electrical charging problems. Maybe it could be to do with the resetting of the alarm after battery disconnection or resetting the remote fob after new battery? Cannot give proper answer as after reconnecting battery it may be 2 to 4 weeks before it happens again.
Is this a factory alarm system or after market?
If this is a factory system insert the key into the outer door lock cylinder and unlock the door this should disengage the alarm system. If this did not work insert ignition key into the ignition cylinder turning it three times from off to on, quickly, and on the third time go straight to the start position. If it is a factory system this will override the alarm and reset the system. If this is not a factory system let me know and we will go from there,thank you.