The phrase "your continued support" is grammatically correct and usable in written English. You can use it whenever you are trying to politely thank someone for their ongoing support, or express the hope that they will continue to support something. For example: "Thank you for your continued support of our local charity.".
Thank you for your continued support, and best regards for a fruitful new year as we continue this historic mission.
Thank you for your continued support of The New Yorker.
I would wholeheartedly appreciate your continued support and cooperation.
Thank you for your continued support, Jim Antol CEO and Chief Bottle-Washer Absterge, Inc.
"To succeed however, I need your continued support, understanding and patience".
"I would ask for your continued support," he told the senators.
I'm calling this evening to confirm your continued support for our next Republican nominee, Herman Cain," the script said.
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