I've had boa lacing for a few years now and although I have not read any 'official' recommendations, my answer would be... it depends.
When just back from a trip I tend to leave them open to let the inside of the boots dry up. When dry though, I tend to close the inner liner, and tighten the boots up to at least as tight as they would be when my foot is in them. Part of the reason is to just make them easier to store/transport, but also so the boot and liner keeps its overall tightness and remains snug next season.
All that being said, my boots do not last more than 2-3 seasons of heavy use and they are ready for retirement (primarily based on slicing to the top of the rear boot supporting the board while on chair lifts) so I do not have any real long term advice.
The lacing system creates its tension based on winding the cable so it is not something that would stretch out from leaving it tight an extended period of time, so I cannot imagine anything other than rust affecting it.