normally this syptom on most is due to one of the doors not being closed fully or a dodgy microswitch in th lock,or just a faulty lock.
not sure on the set up on the MK3,I would have thought it has some type of micro switch.
If it was me I'd just disconnect the wire from the boot lock and try it on the remote again,to try and rule out the intermitant boot lock as the problem.
Im not sure why it locks and unlocks on the remote but works with the key
,unless theres a control box for the central locking which is at fault
hopefully it's just something simple like the boot lock.
Touch wood I've not had any major problems with the central locking yet apart from like you a doedgy boot lock which wouldn't lock.
have you done a search,just to make sure it's not something common.