back of my needlepoint getting fuzzy...solutions?

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Hello everyone! By the way I'm Janie...the one from MN who is trying to start a stitching group in my area (so far no takers). I changed my profile name to Violet Stitches to correspond with my group name better.

Here's my question:

I'm currently doing the background of this piece (this is not my stitching, it's a pic of the completed stitching on the internet).
https://s-media-cache-ak0.pinimg.com/736x/a5/ff/8f/a5ff8f009ab33ed185b1fe544ddbd670.jpg


I do not use Q snaps because I'm a two handed stitcher, so I have this on a lap frame like this:http://www.123stitch.com/pictures/ISD-0042.jpg


I find the back of my threads are getting fuzzy as I move the frame around on my legs to stitch. Is this a problem? Will it weaken the fibers in back until they tear? How do you stop this from happening?

This is my first sizeable piece of needlepoint and I'm not sure if the fuzzing usually happens to people or not.

Thank you in advance for any replies!

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