When you use any client side control and trying to click on submit button definitely values get clear after reloading. so, i'm suggesting dont use submit button instead of use HTML button and invoke server side methods using AJAX or WEB API's .
But still if you want go with existing flow, then you have to keep the selected options on change event into hidden variable and same you get on to page using serverside variable inclusion and once the page gets loaded after submit then you need to reassign values back.
Hope this clears your doubt.
Thanks!
B.Ramana Reddy