Hair Lines on Pattern - Only when saved

If anyone can help with this I would be eternally grateful. I have been trying to find a fix for months now and just have no idea what to do. 

I create patterns using a square  format and then make the repeat old school style by moving and placing the art - anywho... Once done I add it to my swatch panel and tile it to the size background I need. 

On screen it's perfect. It's whenever I save it no matter how I save it the hair lines show up. They also appear in prints and on screen when I use whatever format I saved to wether it be PDF, PNG, JPEG.. wether I export it or save it as such. Any ideas what's up or how to fix this?