Sounds like a bad cable; this could be because of:
Cheap cable (screen is simply conductive coated wound tape, which doesn't have decent mechanical performance).
A cheap connector (that does not have a decent screen clamp)
Cable has been bent too far at the entrance to the connector.
The centre contact pin does not have sufficient freedom of rotation (so it stays static while the ring is rotated) - this can cause stress on the wire to contact point and disconnect the pin from the contact. Note that at certain points of rotation, a mechanical (and therefore electrical) contact can be made so the signal gets through, but the joint is only being made due to the centre conductor being in contact (not properly crimped or soldered) with the pin.
Those are the usual culprits for bad coax performance.