I am having the same problem with my 2009 R/T. I get the single honk and it won't remote start probably 60% of the time over the last couple months since I bought it.
2 things that I've been trying to track to see if these are why it doesn't start sometimes. #1, because of the cold sometimes it detects under-inflation of the tires alert which might be keeping it from remote-starting (could be set so any alert doesn't allow remote start) or #2, because it was or wasn't locked/armed with the remote versus just locked and closed.
Those are just 2 guesses as I don't think its a techincal issue. My dealer was no help in answering the problem and only said to "bring it in".