Update 2, April 11, 11:15ET: Some readers have suggested that the allegedly deleted tweets might have initially appeared as replies to now-deleted tweets, which would explain why they are missing. However, numerous users contacted by TNW rejected this premise, claiming the missing posts were standard tweets.
I'm betting it is something like this, or a related "Twitter did some weird UI change which no one understands again".
If it's not, then it's going to be a bug, and Twitter will apologize and attempt to restore the tweets.
Deleting these tweets isn't in Twitter's interest, no matter how much United pays for ads.
Edit: looking into this a bit more, it looks like it only affects Tweets which have @united mentioned. I suspect it's triggering Twitter's anti-Troll flooding measures, which is clearly wrong.
It'll be interesting to see how Twitter responds, given how slowly they ship any changes.