Im not sure about your requirement, i guess you are using GridClientSelectColumn, to select some rows and you want it to be persisting across pages and on Update. Please try the below is a sample code snippet .
Thanks for your answer, I tried your approach and it is working but for one case: I want to get the SelectedRows in page's OnPreRender, but after the update command it still returns nothing because the Grid's PreRender is executed after the page's OnPreRender. I need some event handler where I can set the seelcted rows which is executed during every postback before the page's OnPreRender method.
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