That game in particular, as others have said, you have to submit your best shot the very instant you make it. I found that one out the hard way too.
But in general, I've found I'm mostly able to avoid the dreaded "your score will not be submitted" screen by:
1) never refresh, never use forward/back buttons. Always launch a game using a link from this site. Launching in a new tab is ok, but...
2) once that game is going NEVER EVER open anything else from the website in another tab/window whatever. You want absolutely no traffic between you and halforums from the time you launch the game to the time you submit your score.