I'm not sure why this would be specific to mobile devices.
In both instances (mobile and desktop) do users start at the same SP website and then SSO to ADFS?
If so, I would expect they would use the same SAML configuration.
Are users prompted to login at ADFS in both instances?
To investigate further we would need the associated error events in the Windows ever log on the ADFS server.
We would also need SAML trace enabled at the SP and the generated SAML log file.
You're welcome to send these to firstname.lastname@example.org
mentioning your forum post.