I've had that problem too and ended up deleting the existing relationship(s) like Blimey suggests so that the point can be moved where it's needed.
What's puzzling is; why does it FIX itself when there's no geometry near it? It just ends up being in some random location.
Is there some switch or option to stop the Point from being fixed ?
Does the cursor change when placing the point? If so go to Tools > System Options > Display/Selection and deselect the Allow selection in HLR and shaded modes option.