I switched the ring to airplane mode on Monday at 21:00 when it had fully charged. It then did its sleep readings that night and the following day on Tuesday at 13:44 it was at 99% battery, and on Wednesday at 14:10 it was at 82%. I had estimated in normal mode it was using around 15% per day so airplane mode is a good half of that although it's a pity I did not run it this way for the whole week to be sure.

The ring remains in that mode until you pop it on its charge and then take it off so nothing is synced but the ring is recording everything on board as normal. When you do sync it nothing is lost. Without airplane mode on it is syncing the step activity every now an again so it is possible to just leave it in airplane mode and sync once a day or every second day. Does look like its battery with then at least last 7 or 8 days instead of the normal 6.