That would be even dumber. It happens and it's a huge deal because it allows the Nights King to find him almost instantly and sets up a harrowing escape, but it only works once? Talk about a Deus Ex Machina moment. "Gee, we need some excitement, let's pull a magical connection between Bran and the Nights King out of our ass and then forget all about it..."
Nope. They damn well better use it again or they should not have used it at all. I'm betting it's something Bran will have to work around and eventually learn to use to his advantage.
In all fairness, they already knew he was there. The White Walkers also knew they couldn't get in there because of the Children of the Forest. All we know is the mark allowed them to ignore the magic protecting that cave. We don't really know if it means anymore than that.