2004 Legacy : Alarm randomly goes off in night!

[PaulColl]

I have  2004 Legacy 2.0 auto which is getting long on the tooth, but has generally served me well.

However, these past few nights I have found that if I lock up the car with the IR button on the key, some hours later the car starts emitting a siren noise for about 15 seconds off, then fifteen seconds on, for up to five minutes.
No indicators flashing - just a siren.
If I try and unlock the car, this works, but the alarm still sounds. I can even start the car and drive it around - with the siren still going, so as well as no flashing lights, this siren noise is not associated with the immobiliser function, either.

On the first night it happened, I hastily got a torch, flipped the bonnet and removed the +ve connection from the Battery - I could see no other way of shutting the car up!
This resulted in the car running very badly the next day and stalling for a few hours - I believe this is because the engine management has to 'relearn' the engine's habits.

Does anyone know what this issue could be?
At present, the only option I have (other than to disconnect the battery) is to leave the car entirely unlocked overnight. Not ideal!

[Greenmamba]

If you lock the car with the key (not via remote) so the car is locked but not alarmed, does the same night-time alarms still sound?

Sometimes one or more door switches, maybe one of the bonnet plungers might be sticky causing the system to think the door/bonnet is open? Worth checking. The only other possibility i can think of is the alarm's 9v Battery needs replacing. Found under the scuttle near the nearside wiper mounting position.