While I was offline for 6 hours today, no research was done and the counter was the same as when I left it. What gives?

There is a limit on the amount of Research Points you can have at any given time. In the 'Research' tab, you can mouse over the production total to see your limit. It is based on your Rank.

Well crap. 600 shy of what I needed. Thanks.

You can spend your points at any time on any research area. You don't need to wait until you have *all* the points to finish it