A hotfix for this issue in 8.1.1 follows:
0000678: Page permissions don't work if a member is in a club - ocPortal feature tracker
Additionally, here is the fix for 7.1.6:
Most users use zone or category permissions rather than page permissions, however for affected users this is a very important fix. It is recommended that all users install it, regardless of whether you think you may be affected or not.