When should you stop using a dating site after meeting someone?

When should you hide your profile on a dating site and stop hosting inquiries after you’ve met someone? Should you put everything on hold, anticipating a positive match? Should it be before or after the first date, or after many dates and sex? Is it necessary to discuss it with the other person? The other person met you there, and will know if you’re still available for others to contact. Will poor judgment at this point be cruel or ruin a good thing?