You have to differentiate between steem and steemit:

Steemit is just the frontend, this may be closed in the future (unlikely but possible), but there are other frontends like busy.org, d.tube, etc. Also steemit is opensource so one would just make a clone of it and let that run. (I had one of those a while ago^^ )

Steem is the blockchain, as long as 20 people are willing to have there servers running it will continue to run.

So no, I don't think steem/steemit will ever close :)
(until the heat death of the universe of course laughing )