Question about Criminal Background / Health Checks

I haven't had to look for a job in five years, but alas, it looks like my time at my current position is up. My visa doesn't expire until the end of February--does this mean that I don't need to submit a new CBC and health check as long as I take a position at a new school before that ends? Or do I need to get that paperwork done over again?

I'm a bit of a dummy when it comes to immigration stuff. Thanks to anyone who can help me out here.