(TL;DR: we don't need them.)
Let's consider for a moment how these things might actually work. From your question it seems that these are navigational beacons rather than a vital part of the FTL process. Why do we need them? How are they used?
"Space," it says, "is big. Really big. You just won't beieve how vastly, hugely, mindbogglingly big it is." - The Hitchhiker's Guide to the Galaxy.
OK, yes, we all know that space is big. What's not quite so obvious is the effects of the vast distances involved. Sitting just outside of Sol's heliopause we can spot a number of pulsars and other navigational reference marks... but due to the speed of light we're seeing where they were 500 years ago (for the closest two) or more. Sure the average deviation over time is low, but it exists... and you have to factor it in for every new location.
And this is where our FTL beacons come in. They broadcast a complex FTL signal that can provide extremely precise positioning information across thousands of lightyears. We can not only figure out where we are but get some idea of the way space is warped between ourselves and the beacon, which is invaluable for calculating a jump route that doesn't end up in the heart of a wandering star. We get almost real-time mapping of spatial distortions in the area as well, which makes our job so much easier. No more plotting a jump against predicted proper motion and getting lost in some nebula or flung south of the galactic disk because space didn't act quite the way we expected.
Which is all well and good, but there are probably a bunch of old-school pilots out there who remember the early millenia when pilots were real pilots, with none of this hand-holding crap. They had to slave over a hot quantum computation bank for hours to get a plot, and half the time they'd end up having to do it all over again when they missed the target. Sure, it was hard. But it was real.
Given enough time and reactor mass, there's nothing really stopping a ship from just jumping around until they get close enough to the target to make the last jump on dead reckoning. While the beacons eliminate the vast majority of uncertainty from the process, they're a convenience rather than a necessity. They're the GPS that tells you exactly where you are rather than the sextant that just gives you a pretty good idea. (Yes, I know, a very good idea when used right.)
So what's to stop someone from blowing them up? Well, we can make it expensive for them to do so, with big guns and so on, but ultimately they're just making life harder for everyone without actually stopping FTL travel. Yes they need to be spanked, but that's why we have Space Navys on speed dial.
If you really want them to quit, make the beacons cheap and easy to produce. Build up a replacement stock of a few thousand and, whenever one goes down, go out and spread some new beacons around the area. If destroying a beacon just means you get five new beacons, it doesn't make sense to keep trying.
Oh, and since beacons are now cheap enough to basically throw away, we won't bother trying to destroy them now. Instead we'll have the bad guys start knocking out repeaters and sowing them through the area. That'll play hell with your navigation, believe me.