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.
See the mobile pin app: https://appstore.home.mendix.com/link/app/2214/Mendix/Mobile-Pincode
Is SSO with Oauth(2) not something you can use for this?