Every time I leave the site, I am asked to log in again. This is new.
So sorry your post has not been responded until now. FamilySearch will ask you to login each time you wish to access the site to protect your personal data. However, you could set the site to remain signed in for two weeks by ticking the box "Keep me signed in for 2 weeks". Only do this on your personal devices.
Thank you for using FamilySearch Community.