So I just finished writing up an SSO document (not yet published, in review) and SSO and refresh tokens are orthogonal. Refresh tokens are used when you have a client who wants to get a new JWT, and SSO is used to transparently log a user in when you are using the hosted login pages.
So I wouldn't worry about the refresh token appearing or disappearing.
... handling SSO in my application but looks like my SSO session is dropped after some short time ~1h, but Session timeout for the tenant is set to 10 days
What does the fusionauth.sso cookie have for the maxage/expires value?