You may find if you've partially refunded a ticket, the ticket is not able to be rescheduled through Sales > Reschedule Tickets. The New Date and Time column shows "This item has been refunded" instead of Upcoming events.
Currently Altru does not allow the rescheduling of partially refunded tickets.
To move the registrant to a different event, you can create an order for the patron for the new event and use a discount to discount the price. If using a program that requires registration, you can also cancel the registrant in the original event.