Re the batteries only lasting a few weeks, sounds as if one of the buttons is shorting out.
Re not locking, could be a number of issues: -
When new batteries are installed, has the key fob be re-sync'd correctly. New key is £149.50 incl. VAT from Main Stealer (ask me how I know)
If not locking on remote, but locking on key, it could be a faulty door lock mech (£150.00 each VAT from Main Stealer (ask me how I know)). Here's the gamble.., don't change it and it deadlocks, you've got to cut the latch bar with a hacksaw, from and through the rear passenger door frame....
For the sake of £50.00, take it to a garage and get the BECM read to find out what's happening...., or not. That way, he can make an informed, correct decision.
Chris