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The NY Times offers 50% off regular rates for home subscription but will allow you to renew at 1/3 off. Looks like you can renew at this rate indefinitely (every 12-13 weeks, that is), but if you just ask them to extend your promo rate, they will almost certainly give you some mumbo-jumbo about why you can’t do this. Don’t bother! Just tell them you want to cancel your subscription, and they will offer to extend the discount (with perhaps a few days at the regular rate).