@pipanebo
Other than the newer offline-first automatic way in preview (for Canvas Apps using Dataverse data source only)
Mobile offline for canvas apps (preview)
it usually doesn't work automatically just out of the box like that unless you set up all of your formulas in a really specific way to make your canvas app offline capable.
Try to check on this guide here.
Use Connection.Connected to decide when to use the offline saved / loaded data, and when to use the data source directly.
Even when using the Dataverse automatic offline-first way in preview, to the extent it doesn't support some specific features, you may want to use this specific way too for those pieces. For example, certain Power Fx functions are not supported with the newer automatic offline-first access feature for Dataverse as you may see from the first documentation link above. For example the functions CountRows, Filter / LookUp on LookUp column, First, In, IsBlank, Relate, Search, StartsWith, Sum/Min/Max/Avg and Unrelate are some Power Fx functions which might not work with the automatic offline mode for Dataverse. These may not be the only ones as well and you may want to check further on your side by testing it.
Anywhere you accidentally still use the data source directly in your formula while offline (and where the mobile offline for canvas apps newer way does not support it automatically) can be causing that message. That includes anywhere in any Control, such as a Gallery Control, that may be looking up something from the data source directly that is not in your collection, for example.
You may need to save data periodically using SaveData while still online, then use LoadData to load it back in whenever you are offline, in this case.
You may want to use a Timer that runs periodically, such as that in myApp Timer Wait Recipe 2023 to help you save data periodically while still online (however, you may want to adjust the formulas, and you may want AutoPause set to false if using a Timer).
If not using a Timer, you may want to periodically save data some other way, such as simply every single time you get the data from the data source when Connection.Connected is true.
Or check where in your Canvas App the newer mobile offline for canvas apps feature may not be supported or working in your case, and see if you can rewrite the formula(s) in a way that the newer mobile offline for canvas apps can support it instead.
See if it helps @pipanebo