First, checks do not expire. They may carry the printed notice something like "Not Valid After 90 Days", but that will not prevent a bank from cashing it. If you replace it, they will be holding two valid checks signed by you. Also, most landlords and property managers cash the check immediately, and record it as a liability.
As to the nonperforming landlord, that may or may not be a valid reason to terminate the lease. You have to ask yourself if the legal expense and your time are worth the possible gain.