Looking in Settings > Battery my iPhone X is reporting that OmniFocus 3 is responsible for 34% of battery use - twice as much as the next thing on the list, and most of this is “Background Activity”. On my iPad Air 2 and my son’s iPhone 5s, OF 3 background activity is also (by far) the greatest battery hog. Is anyone able to shed light on this? 
Have you contacted Omni to ask if they have a solution? In the Settings area there’s a Contact Omni button which will open up a new mail telling them which version you have.
Thanks Rose. I’ve just done that. I’ll report back what they say. 
I haven’t forgotten to report back … I just haven’t had a response yet.