Feedback and appraisal requests will remain open until you have processed them as coach. Sometimes however, it may occur that there is a pending request that isn't relevant anymore, because the program has ended, for example. In that case, the trainee's enrollment should be closed to delete the request (note: the trainee won't be able to complete new Role Plays anymore).
Only an administrator can close an enrollment. You can do so by going to the program, clicking on 'trainees', select the trainee and then click on 'close'.
If you don't have an administrator account, ask the project leader at your organization to close the enrolment or ask them to contact TrainTool.