Oh yeah, The squirrels here have tried everything to get onto mine. Had a 1/2" woven nylon aircraft tie down rope holding it up. They finally figured out they could chew through that, so now have a chain wrapped around a tree limb holding it. I've had a Squirrel Buster Plus for a couple of years, and it's a lot like the one you have.
http://www.birdwatching-bliss.com/sq...rd-feeder.html
Watch this video. The first 3 min. has lots of good bird audio and video, then starts the squirrel action.