I would say that if an object that has a spell cast on it breaks (such as a tanglefoot bag) then the spell ends.
This can be easily evaded by casting the silence on a stone that is then stick it to the bag. In order to be rid of the silence, the mage has to get rid of the stone.... which is a lot easier than scraping off all of the goo from the tanglefoot bag, but not trivial, either.
It also takes longer to prepare it this way, too; when the PC's see the silence spell cast, and the stone shoved inside the bag, they'll know what's coming the next round, and will have time to try to counteract it.