Before postback or on the selection of value from the dropdownlist; store the selected value from the drop down list in Session variable or nin ViewState variable.
Then Whenever there is post back;
is called. In the same event of the page you need to fill your dropdownlist with the values and after the same values have been populated into the dropdownlist, then with the help of JQUERY you can set the selected value for the dropdownlist from the state variable in which you have earlier stored the value before postback.
**I don't know when you are filling the dropdwonlist; So i have suggested you a solution which you can apply or you can continue with your own method and appending my solution of keeping the selected value in the state variable with your own solution.
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