Sponsored posts, premium themes, promoted posts. Pretty sure they're far from profitable, but they're bringing some revenue in.

http://www.quora.com/Tumblr/How-does-Tumblr-make-money

http://www.businessinsider.com/tumblr-revenues-2012-9

If they are not profitable, it means that the downtime is actually improving their financials...;)

Chuckled at that, given their scale I'm sure they are already at fixed rates for colo space and bandwidth.

- Brand spotlights

- Sponsored radar posts (ads)

- Promoted posts (for all users)

- Premium theme shared revenue

- Selling access to data

Love to, but Tumblr's site is down… so I can't check.