A third season of K-ON! has been indirectly announced by way of DVD pre-orders for the title opening.
Amazon (and other retailers) have begun listing future K-ON! DVDs far in advance:
けいおん!!(第2期) 9 (Blu-ray 初回限定生産) [Blu-ray]
K-ON!! (Season 2) 9
This obviously suggests at least 18 episodes (unless it came with only one episode per disc, which at $70 per disc would hopefully be unlikely), and a second season of K-ON!! (with two exclamation marks), both pointing to a continuous run of two 12-episode seasons, for a possible total of 24.
I agree. But I think the short series is what made it more attractive for me in the first season. I don't get that 'can i be bothered' feeling i get with some other longer ones, though 24 is still short compared to many others.
Just the first scene with Yui playing 「わたしの恋はホッチキス」 was enough to get me back in the mood for this (since I didn't like the second half of season 1 that much tbh). That was a great opening scene for the first episode of a sequel.