Wouldn't a time check fix this? Enter/leave within 10 minutes, no charge. Enter/leave outside 10 min window, charge the exclusion fee.
Obviously, this is not a realistic solution - building new exit gates is simply not worth it.
Practically, such behavior if done repeatedly can be detected as an anomaly in card usage patterns, and a human reviewer can surely figure out what you're doing.
Absent some sort of ranged tag detection (e.g., NFC or RFID), exit determination is exceedingly difficult. I'd argue that NFC/RFID operating beyond a few cm range are themselves a major infosec threat and privacy invasion.