If the service plan has ever been delegated to the reseller(s), then it becomes impossible to delete subscription period from it. An attempt will fail with an error:
This Subscription Period is used in Delegated Plans.
The same error repeats even if this service plan is deleted from the list of delegated and the resellers get synchronized.
An issue is reported as bug with id #PBA-34816 ("Subscription period cannot be removed from delegated plan.").
You may set this subscription period as inactive.