Have no fear...Burn Notice WILL be renewed for a 7th season. I can say this with almost dead certainty.
When a show has been on the air as long as Burn Notice has, it's safe to assume that no news is good news.
Several factors contribute to the conclusion that there will be a seventh season.
1) They've reached an agreement to film in the convention center for one more year "should the show be renewed." They wouldn't have gone to the trouble of reaching such an agreement if a renewal was unlikely.
2) Most of the major stars have said that they want to return.
3) Jeffrey Donovan has thanked fans for "making season 6 the most watched." Very good sign.
4) The BIGGEST factor that points to a seventh season is, as I said, no news is good news. Once a show has been on the air as long as Burn Notice, it is unlikely that the network would cancel the show without allowing them to do a proper sendoff, a proper series finale with events leading up to it. Granted, there are some exceptions (I'm looking at you, Law & Order, but even in that case, Law & Order was not a serialized show the way that Burn Notice is). However, even if, God forbid, Season 7 were a shortened season to give them such a sendoff, USA has, from what I've seen, done a good job of advertising that a show will be entering a final season.