AirNomad, I don't think that the other Avatars will steal her away or anything. Remember that Aang is their reincarnation, and that even if they are not Aang per say, they are all in one way the same person. By causing him pain they are also hurtin themselves. It's the same reason you would have trouble cutting your own hand off.
Besides it seems a little childish to simply remove her from him. It reminds me of a parent scolding thier child for not doing his homework by taking away his TV previliges. This is no way to teach anyone a lesson, that would simply anger him and make him want to be with her out of sheer spite.
Aang needs to come to the conclusion that it is simply better for the world as a whole if they were not together. The Avatar's life is filled with danger and peril, and it would be a lot easier for both of them if everytime something happened they didnth have such strong emotions towards one another. In the end, it will only result in pain.