[Christien]

If the pull-up piece on the sill is just falling without any pressure being put on it, then yes, it's likely the latch which is the problem, as that's where the tension comes from. Though it's possible the problem is elsewhere. First thing to do is pull off the door panel and have a look around. If you do have to replace the latch, it's no fun. Cheap, but a PITA.