Monitoring is part of the ongoing service FUSE provides. A problem can occur, for example, if a webservice isn’t available or a vendor updates their API which breaks FUSE’s connection to your content.
First, no worries — your users won’t notice anything amiss. FUSE will continue to seamlessly use the latest successful index of that content. The index won’t have content that is new between the time of the connector outage and the search being conducted, however.
Next, we get alerted when this type of thing happens. Nine times out of ten, the problem fixes itself at the next indexing attempt. If something really is down, however, it’s up to the FUSE team to get it running again — the are no fees or development costs. This is part of the ongoing service you’re paying for.