Update :
OK. I have another similar power supply ( 12V 3A with 17Ah battery ) in another room for a non-critical function.
Have re-routed that to the problem system.
Before power-on, the supply is 13.19V
After switching on all components of the home system, dropped to 12.91V and registering 1.2A
Has remained constant for 30 minutes now.
So I guess that if it remains stable for the next hour, I can safely assume my old power supply was faulty.
Thanks to all for the input. Really appreciated.
Update : 2 hours and no change at all 