I just recently started using my gmail account after moving a couple of domains over to google due to GoDaddy deciding to start charging a monthly fee to have an email box attached to my domains. I had the same problem of K9 working for a brief time and then it would no longer download new mail. After a little digging I found some info, that being adding "recent:" (without the quotes) in front of your username would force gmail to give it up. Lo and behold, that actually worked and now K9 is behaving properly.
Give it a try, I'm no expert but that worked for me...