Hi Brenna,
You can use a SplitView instead of a Drawer, as suggested in the following forum post:
http://www.telerik.com/forums/keep-drawer-open#tq7Yo9ejPEOsMzUluxb1Aw
I have put the example in a dojo, so you can inspect it with the Simulator:
http://dojo.telerik.com/uMAki
The mentioned Pane's collapsible option is now a built-in one:
http://docs.telerik.com/kendo-ui/api/javascript/mobile/ui/pane#configuration-collapsible
I hope this helps.
Regards,
Dimiter Topalov
Telerik