Mazda 6 Central Locking Problem

[MikeRaw]

I have an 03 reg Mazda 6 TS2. The central locking has had an intermittent problem for a while now, but recently it's getting much more regular. The unlock and alarm on/off buttons work fine. However the lock button doesn't. I have replaced the battery in the key fob, so it's not that! Sometimes it takes around 10 presses before the central locking finally registers and locks the car up. When it does finally kick in there's no problem - all the doors lock correctly as does the boot. I thought it might be a faulty sensor but wouldn't that affect the unlock action as well?

Possibly also relevant - a couple of years ago the car alarm would suddenly go off for no reason. It would be sat on the drive and typically in the middle of the night! Since then I've just turned the alarm off and let the immobiliser do its job alone. My local Mazda dealer couldn't suss it so I've left it alone. Seems to me these problems could be related?

Any advice gratefully received

[GAjon]

Will it lock and unlock manually with the key in the lock cylinder?