I get frustrated when I select some text PopClip appears, but I accidentally move the mouse too far and PopClip disappears as it is designed to do. Is there a way to make PopClip reappear if I move the mouse back over the already selected text?
Yes, there is. In PopClip preferences there is a Keyboard Shortcut option. Set a shortcut here (I personally use ⌃⌘P). Then when you want to show PopClip again, just press the shortcut.