Just a wild guess,:
If you look at the assy navigator while moving with the by constraints option, you will notice that NX does create constraints that in the end gets deleted. Maybe this creation isn't possible for some reason.
It took a while but between a couple of us here we finally reproduced what you're seeing and while we can't be sure that this is what's causing your problem, we at least found ONE scenario which you need to make sure is not what's happening with you.
Anyway, go to...
Tools -> Update -> Interpart Update
...and see if the 'Delay Assembly Constraints' option is toggled ON. If so, toggle it OFF and then go back and attempt to 'Move' your Component(s).
John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA Siemens PLM: UG/NX Museum:
To an Engineer, the glass is twice as big as it needs to be.