Sharpies are made with alcohol-based ink, and alcohol happens to be the perfect solvent for cleaning up dried acrylic paints. So what's really happening is the tip is getting gunked up with re-wetted paint.
I'd bet you could give the tips of those sharpies a brief soak in some isopropyl alcohol, and/or a firm wipe with a wash cloth or paper towel soaked in the isopropyl, and they could be somewhat recovered (assuming they have plenty of ink in the tank)
That being said, I still would not recommend this practice. Better off with a paint based marker or something.