Squirrels aren't necessarily small - fox squirrels can go up to three pounds (as heavy as many hens). And they're big and have big heads. The first time I saw one, I thought it was a woodchuck or capybara.
Be that as it may, if something is pulling chickens through the wire, better wire is needed. A lot of people use hardware cloth along the bottom of the sides, where it's easiest to grab a chicken, and then chicken wire on the top of the sides and over the top of the run. It depends on what you can afford. Also make sure that nothing can reach them on the roost.