Hi Robert -
We've investigated this issue and we have came to the following conclusion:
The problem lies inside the jQuery Mobile default behavior.
When user clicks selectmenu button new menu is displayed.
If this menu height is more than screen height then this menu will be displayed on a new screen. When user closes this menu event "Page Show" is triggered and all select menus are reseted.
Workaround 1: Select "Native" checkbox in selectmenu properties (as you already did);
Workaround 2: Move JavaScript action from "Page show" event to "Load" event. In such case selectmenus will be changed only once (when user loads this page for the first time);