I have the following code
//included all jquery related stuff ..not shown here
I came across this question because I was having the same problem as OP.
Mooed Farooqui's recommendation to reinitialize in Ajax success worked, but not initially.
Ended up that I was also calling the datepicker function in my equivalent of my_ajax_stuff.php. After I took that out it worked perfectly on button reload and postbacks. Hope this helps someone that stumbles upon this old question...