On occasion when I start my 03 wrx there is a beep, which is the same as you get on occasion when you open the boot without unlocking the car. Or when you try and start it when the immobiliser has re activated. Looked in the manual and had a search with no luck.

Any ideas?

 

Battery low warning.
When you start the car the voltage drops and that causes the alarm to beep.

You can check the battery voltage by pressing 8 on the keypad with the ignition on, but car not started. Then turn the ignition off straight away and count the flashes from the alarm LED. 1 flash/volt

If its only every now and then Id say your battery is just on its way out. Probably happens more on cold mornings. So either battery or alternator not charging. My money's on battery.

 

As above. The same thing happened to me last year,changed the battery and it was fine.