There are probably 3 main things that can go wrong in updating the data of the HondaLink app. 1) Honda's servers could be down; 2) there could be a SNAFU in the app; 3) the car could have trouble connecting to the server due to a weak cell signal. Here's my advice as to figuring out what the problem is and how to resolve it if possible.
Scenario 1 - Honda's servers are down
How to know: log out of the app (hit the 'home' icon and then the person icon and sign out) and then try to log back in. If the servers are down it will not allow you to log back in. Also, like today's apparent server outage, several people will mention it on the forums.
How to resolve: no option but to wait for Honda to fix them. They appear to have gone offline several times in the past few weeks, for a few hours each time.
Scenario 2 - Something wrong with the app on your device
How to know: Some fields update and others do not (the servers would have to be receiving and sending data out if some fields are getting updated info); app fails to get updates on one device, but other devices connect without an issue; seems to not update for long periods of time, and people on the forum here are not discussing it as an active widespread issue.
How to resolve: if using Android, go to settings > Apps and find the HondaLink app on the list and then select it and hit 'Storage' and then tap 'Clear Data'. When you restart the app it will force you to log in again, but it should resolve the issue. Not sure how to resolve it on Apple devices; possibly need to delete the app and reinstall it.
Scenario 3 - Car is not updating data to the HondaLink server due to a weak cellular connection
How to know: Scenario 1 and 2 do not appear to apply or the fixes do not resolve the problem. The UI display may show low/no signal.
How to resolve: If you are in an area where this is a chronic problem, there may not be an easy fix. Some cases, there may have been a server hiccup when the car attempted to send data (like when it was shutting down). Try turning the car on for a moment and then after it fully boots up, shut it down and it should re-send data. If the connection is strong enough it may resolve itself. Otherwise, you may have to wait until the car gets into a better reception location, or set up a wifi connection (?).
Just brainstorming here. I may be missing some facts, or obvious alternatives, but this is what I have deduced from my occasional problems with HondaLink failing to update.