I had the sync/save issues described here for around 6 months. I'd lose entries, sometimes right before my eyes. It was frustrating. I have an iPhone XR with iOS 15.5.
A few days ago I uninstalled and reinstalled Evernote, as suggested in this thread, and it's like a completely different program now. It syncs/saves reliably every time.
July 19, 2022 Update: The sync/save problem seems to have returned. Reinstalling the app again doesn't seem to correct the problem (BUT see new twist below). It definitely seemed to change things when I originally did reinstall the app. It seems like a mixed bag.
August 4, 2022 Update: I removed the app, powered off my phone and THEN reinstalled the app. This definitely fixed the problem and it works well now. My theory is the app has a bug (a memory leak maybe for you software engineers) which accumulates over time and then it starts to operate poorly. Reinstalled AND powering off the phone clears things out.