If I log in into the data SE, it always forgets my login credentials. I have to log in again and again.
I think, the feature is available in the other SE sites, and maybe it wouldn't be very hard to import it into the data SE code as well.
This may happen some day, but not without a tremendous amount of thought and likely time. The problem is that Data Explorer is open source (https://github.com/StackExchange/StackExchange.DataExplorer), which means we can't just plug in our authentication pieces. It's quite complicated, and from the SEDE point of view: a lot of baggage for anyone not us.
Maybe one day. Since we're now using cookies for auth up on the second level domains (to prep for the child
meta.* moves long ago), it's at least closer to possible.