How long does an employer have to terminate you after a positive drug test?

Technically yes but it would be really stupid to do so. The reason you get suspended for a positive screen is to give you time to dry out. After three months it's more of a retaliatory move, and those are illegal.

On the other hand, he's perfectly within his rights to fire you after 3 months for failing a drug screen, if "drug test failure" is a termination offense at your company.