Stay connected to what? Your wifi connection? No, certificates have nothing to do with the connection. If the M Preview doesn't stay connected, report all the particulars (your device, all your settings, everything you do) and revert back to Lollipop. Evidently there's a bug. (Of course you've tried at least 4 or 5 different routers, including those set to fully open, right? It could be a TKIP bug or an AES bug, so they'd want to know if it loses ALL connections or only a certain setup.)