So our access token is valid, but just not valid for this particular url. It seems therefore that we need a user access token and not an app access token for this particular feed
Due to the permissions per type of access token, you do need a valid user access token in this particular case. Read all about access tokens and types. That's just the way it is.
This page describes how to get the elusive user access token by redirecting the user to the auth dialog and asking for the relevant permissions but we need to achieve this without interaction from the user and the user has already given our app all the permissions we need.
If your user already has given his/her permissions, why are you struggling then? I suggest you persist the user access token. From this endpoint:
https://www.facebook.com/dialog/oauth?client_id=..&redirect_uri=..&state=..&scope=..&response_type=..&display=.."
you retrieve a code, like this:
YOUR_REDIRECT_URI?code=OAUTH_CODE_GENERATED_BY_FACEBOOK&state=YOUR_STATE_VALUE
Use this code to generate your user access token, as explained here:
https://graph.facebook.com/oauth/access_token?client_id=..&redirect_uri=..&client_secret=..&code=..
This will result in a response like:
access_token=USER_ACCESS_TOKEN&expires=NUMBER_OF_SECONDS_UNTIL_TOKEN_EXPIRES
There it is, your user access token. Persist it. As you can see it expires after the value indicated in the response. If you are using the new API, it should indicate 60 days (that brings me back to this: offline_access is deprecated and results in short-lived - valid for 2 hours - tokens), link. Whenever your user logs in to your app and uses the Facebook integration, the tokens gets refreshed to again, 60 days. This means, that IF your user should not login to your app and use it for 60 days, it will expire.
You can check whether the user access token is expired with:
https://graph.facebook.com/debug_token?input_token=INPUT_TOKEN&access_token=ACCESS_TOKEN
If that does: renew the user access token by using your app access token, it is well documented right over here. But I'm quoting this part:
Server-side Login
To obtain a fresh [user] access token in this case you must pass the user through the full server-side Login flow again. However, assuming the user has not de-authorized your app, when you redirect the user to the OAuth Dialog, they will not be prompted to reauthorize your app, and will be immediately redirected to the redirect_uri. This means that the re-authentication process can appear reasonably transparent to the user.
Bottom-line: there are no user access tokens that are valid for ever, the app access token however is. Persist your user access token and check whether it is still valid before performing API calls with it. A normal user should use your app within 60 days and should not just de-authorize your app for fun. Hence the use case in which the user should re-authorize is fairly rare, however, you need to expect it.