No excuse. I've overstayed my insurance for the last 3 visits, and taken out additional cover each time. It's more expensive to take out cover while you're already away, and limited to specialist companies, but such is life.
Every "annual multi-trip" i can remember has been limited to 30 days per trip too, so if staying longer, you need different cover. It really isn't rocket science.
There's no excuse, and no sympathy, for being uninsured.