I am having this issue too. Been going on for weeks. When I go to bed I have to close Connect as it murders my 6S+ battery. After about 8 hours my battery will have gone from 100 to less than 20%. The attached screenshot is not really indicative of how bad this is, as I turned off Connect about 8 hours ago because it was murdering the battery. More rather I would have uploaded it, but kept getting an error... Out of a 24 hour day, nearly 16.5 hours of the battery was associated with Connect.
And no. No GPS, unless Connect is keeping it active without my knowing it.
I'm getting similar results. I think it's probably linked to Livetrack in my case, but having said that I can watch the percentage drop as it's syncing at the end of a ride - 9% lost in a minute or so at the end of this morning's ride! I'm using an iPhone SE (iOS 12.0.1) paired with an Edge 1000. I think the problems started with the recent release of Connect 4.12, but I'm not completely certain.
I encountered the same issue with my older iPhone 6s on iOS 12. Maybe it was the same under iOS 11 but we didn't have such a marvellous battery usage analyser then. Having switched to an iPhone Xs everything is under control now. Maybe because what was draining battery is now performed much more efficiently or just because the battery lasts longer.
I’m using a iPhone 8 with Garmin Connect and a Vivoactive 3 (all with the latest versions) and was having a battery drain issue as noted above. Connect was running in the background, even when it was swiped up and not open. What I discovered was that the Apple Health App was using Connect as a source. I’m not sure how that happened - I do "play" around with my phone so I might’ve done it without realizing it. Anyway, as soon as I turned off Connect as a source for the Health App, my battery usage went back to normal.
If you're not using the Health app, you might try this "fix".