I think you're right about him not being motivated, but I suspect it could be a number of other factors and that would only be speculation.
Like I said, if he was only here to win the Champions League (No doubt that was one of his main goals), then he would have considered his options and looked to the exit door, and although we have no idea if that did or didn't happen, he's still here so he must have seen a short-term future as a realistic option.
Right now, Henry, from an outsiders point of view, doesn't seem to have the most amazing personal life, being away from his daughter more often than not, he may not be happy for that reason.
Secondly, the recent handball-fiasco which was taken completely out of context by the British press going to town on him and making him public enemy number 1. That has obviously taken it's toll on him and it has still happened very recently so getting over that will take some time.
Thirdly and the last point I can think of at the moment, is his own reflective evaluation of where he belongs in football and in the best team in the world. At 32, he has been declining for a few years now, but in some ways he turned back the clock last year, making a real contribution and not just being some bit-part player. This year he probably felt he may be able to achieve something similar and at the moment it's not really working out, so it's possible that he has hit somewhat of a wall in self-confidence.
I feel this will be his last season, successful or not, he won't be here after the world-cup.