I would like to provide the initiator with the ability to cancel a request for a period of time before the next person processes the request. Is this possible?

use Pause for action

I guess initiator doesn't loose permissions all of sudden. likely you change his/her permissions within workflow. if you perform permission change after pause action elapses, initiator should still have at least edit permissions on an item/request created.

then it's just matter of implementation how do you handle 'Cancel request' event.

eg, initiator might change a status flag in request form, that you will check then in workflow.

or he/she can completely delete item/request

or you can create cancellation workflow, put it in right click menu and from within the workflow terminate paused workflow

if you have sufficiently experienced users and provide them with sufficient permissions, you might even show them how to cancel running workflow.

etc.

technically it would be possible to cancel a request even in case initiator doesn't have sufficient permissions anymore, but you are then left just that additional workflow option, and you have to make sure that the cancellation workflow runs within other privileged (service) account.

hm, originally you asked

to cancel a request for a period of time before the next person processes the request

now you say

I am not sure what needs to change in order to give the initiator of the task the ability to cancel the task.

these are two different things (at least as I understood it).

I understood your original question so that you want to delay creating of a task so that initiator might revise the need to approve request/item, and so that approval task is not even created.

to cancel already existing task you have several option, eg.

- you can teach initiator how to cancel workflow. that will cancel the task and overall approval as well

- you can create one another workflow that would take care of identifying what task is running on a given item and terminating it. have a look on Complete Workflow Task action. initiator then just need to start that additional workflow.

- in existing workflow you can create a parallel branch to flexi task that will wait for some specific event (eg. setting on some 'request cancel flag' field), once the event occurs it terminates the task