Access token keeps expiring after few hours

Dropbox is in the process of switching to only issuing short-lived access tokens (and optional refresh tokens) instead of long-lived access tokens. You can find more information on this migration here.

Apps can still get long-term access by requesting "offline" access though, in which case the app receives a "refresh token" that can be used to retrieve new short-lived access tokens as needed, without further manual user intervention. You can find more information in the OAuth Guide and authorization documentation. You can find an example of using a refresh token to get a new short-lived access token, without manual interaction, here, under "Example: refresh token request".

For reference, while the creation of new long-lived access tokens is now deprecated, we don't currently have a plan to disable existing long-lived access tokens. (If that changes, we will of course announce that ahead of time.) That being the case, you can continue using existing long-lived access token(s) without interruption, if you have any. Also, note though that after the change you won't be able to create new long-lived access tokens.