I don'e see such performance counter readily available in the system, Anyone having SMT connection to PI server can easily see the gaps which system marks in red under "Archive" tab.
Can you let us know what is your use case which can not be achieved by looking into SMT?
Its kind of triggering alert based on such performance tag and not everyday going to SMT and checking for archive Gap
As Siddhartha J said, there is no such performance counter tag available. But we have the tuning parameter MarkArchiveGaps, which returns special Arc Offline events when archive files are taken offline or when time gaps are detected in mounted archives. The archive offline markers are primarily used to prevent any misinterpolation of data across missing archives.
You can enable that Tuning parameter by navigating to, PI SMT-->Operation-->Tuning Parameters-->Archive-->MarkArchiveGaps-->set it to 1 and restart the PI Archive Subsystem.
You can monitor the Archive Gap using PI Processbook or PI Vision Trends.
If you want to know more about the Archive tuning parameters, please refer to the below link,
How often are you registering and "unregistering" archives? This is a bit of a strange request as archive gaps aren't typically encountered during normal operations, but encountered when work is being done on the PI Data Archive (reprocessing archives, registering old archives, etc...).