Why does Private Only plugin keep throwing me to the login page (post migration

We are using the Private Only plugin, and it works fine for us on other sites, and worked fine for us on this site until we migrated to a new domain yesterday. Now I periodically (sometimes every reload) get thrown out to the login page in order to see the site. This usually happens after I try to edit a post in the backend, or view a post after I’ve edited one, or generally try to do something in the backend.

Frontend (P2 theme) doesn’t seem to throw me out as often (can’t remember a time, actually)

So I’m thinking this has to do with the migration, not necessarily a bug with the plugin or anything, but don’t know where to edit/look. Any thoughts? We really have to have this site be private.