DISCLAIMER: I am not in the beta, but I did code the physics of the grappling hook in both the T1 and T2 Vengeance mods, and I believe it's quite accurate. So even if I'm not in the beta, I do have experience with something that is at least very close to the T:V grappler.
That being said, the problem here at hand is very similar to two things already in the game. The jetpack (as mentioned earlier), which runs out of energy if you use it too often and for too long, and the chaingun, which gets less accurate the longer you whore it.
The problem with the grappler is not that people use it too much before they hit an inv. The problem is that they tend to use it too frequently. The jetpack and the chaingun are perfect examples of balancing something that is not to be used too often (sure, the CG has ammo too, but you never use up all of it at once). The grappler needs some kind of system that limits its whoring, but keeps it usable over time.
My suggestion to the problem would be a little tinkering with line strength. Every swing would stretch the line more and more (not affecting distance though), and it would snap if the tension's too much. How is this different from the current system? The line would need time to get 'unstretched' after a swing, much like how the CG has to cool down after each burst. This way, 3 or 4 swings after each other would still be possible, but after that the rope would be very likely to snap.