Storing Drupal form values when using tablesort or paging
No there's no in-built way around this. The tablesort and pager functionality works by providing links to new pages. When you link to a new page, any values you have in form elements on the previous page will not exist any more, unless they've specifically been persisted to the session and then picked up again on the new page load (this is a browser issue and nothing to do with Drupal).

The easiest thing you can do is implement AJAX for your pager/sort links which invokes the content area of the page to reload rather than navigate when they're clicked. Then your form elements will remain untouched.