According to Sony Online Entertainment, only accounts that are active and in good standing on September 15th will be eligible for the sunset period and events, so if you want to play, you'll have to plan ahead and reactivate your account one last time to make sure your account is active on Thursday. After that, your account will remain active for free until December 15th, when the galaxies are closed down for the last time. Confused? Mepps on the official forums has an even more detailed explanation for all the caveats and what-ifs you can dream up.
Players meeting the criterion will also find that their accounts are flagged for free access to other SOE games (including EverQuest II and DC Universe Online) from October 15th to the end of the year, further sweetening the deal.
Finally, although the SWG TCG will remain in operation as long as the game does, loot cards cease being redeemable after September 15th, so grab your free loot cards while you still can!