There's nothing more frustrating to me than being almost but not quite on the Internet, as I discovered today when going to a cafe (unnamed, but linked) which advertised free wifi. My connections were slow and unreliable and frustrating to use. It looks like you're online but any applications that depend on always-on Internet for their well being work out badly.
The best reaction that I have for this state of interrupted connectivity is to go offline and write in my little notebook. I've written before about Pocket Twitter; there's also a very effective Pocket Issue Tracker where you write down things to do and then re-sync them with your online issue tracker once you are online again.
There is technology that will help this state of interrupted connectivity, and I use it when I can. Of all of the applications that I use, Gmail and Evernote are the two that have the best developed clients that can intelligently buffer things when you're offline. If I have my laptop and no connectivity, I can also use "git" and "vim" to work on my writing projects, knowing that a "git push origin master" command will resync when I'm ready to update changes.
Once upon a time there was no internet and every application worked well offline. Netnews was delivered one batch at a time, and you'd read it while the modem was quiet; email, if it was important enough, might warrant a long distance call to deliver. Now, when the net is down or flaky you should still be able to get work done. And yes, I should really get a data plan for my new phone so that I don't have to rely on the quality of random coffee shops for personal productivity.