Hi Peter,
With the latest Mendix version the mobile app will automatically log you in if you have already. There is a token placed on the users device which is used to authenticate them and set up a new session.
Which version of Mendix are you using? Cause this should come out of the box with the latest version and mobile build.
Regards
Simon
See the mobile pin app: https://appstore.home.mendix.com/link/app/2214/Mendix/Mobile-Pincode
Regards,
Ronald
Is SSO with Oauth(2) not something you can use for this?