Persistence of Ethereal Bonds

Had an argument at the table tonight about what happens when Ethereal Bonds is destroyed (" At the end of the Environment turn, this card deals the Hero Target with the highest HP 2 Energy Damage. A Target dealt Damage this way cannot deal Damage until the start of the next Environment turn.").  One player argued that, since EB was gone, the "cannot deal damage" effect was also gone.  But it seemed to me that it should still persist until the start of the next Environment turn.  I can't quite articulate why I think that, however, so I could perhaps be wrong.  Opinions?

Anything that has a specfic time limit stated on the card takes effect for the entire time limit regardless of whether the card remains in play.

Otherwise Mistbound would be useless.