I had the same problem and while some of the above solutions work, the easiest fix of all is to add this to your css:
#ui-datepicker-div {display: none;}
This basically hides the realigned datepicker element when it cannot be binded to an existing invisible element. You hide it, but it will be initialized again when you click on an element that needs to display the datepicker. Upon re-initialization, the datepicker element with id #ui-datepicker-div will have the correct position.