I usually suspend my session when I'll be away from the computer for a while. Then, when resuming the session, CheckGmail tells me that it couldn't contact Gmail.
I suspect that CheckGmail is trying to update its status immediately when the session resumes (even before I've had a chance to type in my password), before the network interface is back up and running.
It would give it a cleaner impression to the user if it could detect that the network interface is down, and wait until it comes back up before looking for new mail.
It's not a major functional problem -- it just looks a bit sloppy when I wake from suspend and see a broken CheckGmail icon in my tray.
Otherwise it's a great tool!