Good points raised. Always a possibility their lender doesn't approve mortgage, renovations are delayed, etc. Perhaps I am overly sympathetic to the tenant's situation and should just tell them to vacate in 60 days so I can get my new tenant in, as John-PA-LL suggested.
We made the mistake with our tenant allowing them to stay a couple months which caused us to miss the prime college market. In your situation. I would probably just raise slightly the rent and say the lease has to run instead of Jan, March which is a much better time to start looking for renters. and after March can go month to month.