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.
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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.