If you find that this is not the case for an active/lapsed gift, then the permissions have not been enabled for the Donation Form corresponding with the user's gift.
The users can not modify their sustaining gifts in the Service Center because the donation forms have not been configured to allow them to do so.
You can verify this by:
- Go to Fundraising > Donation Management
- Click All Donation Forms
- Click Edit for the specific donation form
- Navigate to Design Donor Screens
- Select Configure Service Center (it's under Related Actions)
- There are a series of checkboxes at the bottom that need to be configured to allow the donors to modify their gifts