Same issue - iPhone 6s Plus, latest OS, not jailbroken. Last sync was May, when I switched phones.

After restoring the app from the backup, did you have to login to your Fuelly profile?
Did you also restore from an iTunes backup?

I restored from iCloud, not iTunes. Is there a way to export the data and then import it, without manually keying in all the fillups?

I restored from an iTunes backup.

Were you prompted to login after restoring the app (first launch)?
Same question as above^
At the moment... not without some editing of the CSV file. How many fillups are you needing to re-add?

Yes. It popped up after my first launch of the app to enter a new fuel up.

My export basicly shows the 2 fuel ups I have entered since switching devices have not been synced and don't have "ID's"

The actual login page or just the "Logged Out" error message?
Since you only have 2 fillups, can you please log out of the app completely (Settings-> Log Out) and then login again, and enter those 2 fuel ups?
Please let me know if the Logged Out error message comes up again.

I got the logged our error.

Well I didn't read your instructions very well but this is what I did.

I logged out of app deleted it.
I logged into the site and entered my 2 fill ups.
I reinstalled the app and logged in. It synced up and is working with no error.

Sorry I didn't log out and then log back in to enter the fuelups.
This probably won't help

But I appreciate you help. I am glad that mine is working again.

Anyone still experiencing the "Logged Out" error message?