What type of task is it, and what is it trying to do?
Most server tasks in ePO that require credentials allow you to edit them, so it may just be a case of identifying where.
The task will be run as the user that has saved it the last time. So in order to "re-assign" a task, the task must be edited by the new user. I always schedule pull tasks etc with the built-in admin account, which normally won't be deleted