The last user who started the batch/recurring processors must be an active user. If this user is made inactive, then the batch and recurring processor will not run, but the next run times will continue to update.
Have an active user with appropriate permissions (eg: Systems Administrator) to stop both processors and restart them a few seconds later.
There is a workflow that can be activated for when the batch processor is not running to make sure online and manual payments go through the matching process. This workflow does not activate the recurring processor so recurring payments will not be created by this workflow
We strongly recommend having an ongoing staff member with appropriate permissions (eg: Systems Administrator), especially if you have staff change overs to stop this issue from occurring.
Unfortunately, due to Salesforce security requirements, there is currently no workaround for this issue and will need to me managed procedurally.