In working with the online RadScheduler Demo: Scheduler/Client-side Events
, I reproduced that you cannot select an appointment in Week or Month View and enable the resize arrows to drag it over a multiple-day period. This can only be done in the Day View.
However, if you enable the Timeline tab, you can resize an appointment across multiple days. Then, when you switch back to Month View, the appointment retains its new resize.
Does this help?