Hello @Bishop, Mike S ,
One quick observation - The Logic App is failing after certain period of time for successive request - as per screen shot > 12 hours. I am assuming that you are signing in again in order to rectify the error.
Logic App getting INVALID_SESSION_ID from Salesforce - usually indicates on a token / session expiration that is set in the Salesforce environment. (Or IP Restriction in some cases - but may not be your case as it works for certain amount of time) . There are few configuration that can be set up at the Salesforce end which can expire the access token (as well as the refresh token).
I would recommend you to check for the session restrictions. Attaching image for your reference. Managed to get some screenshots from internet but may actually vary at your environment.