I seem to remember there being a plugin or external application that saves all of your lap times automatically. I can't find anything trying to search for something like this though. Does such a thing exist?
Well, kind of ... you may create a folder "times" in your RBR installation folder.
After each stage, one or more "txt" files are written containing the car, checkpoint and finish times.
Maybe worth a try.
Also the Chrono-something feature is included in RSRBR (if you're using it). If enabled it automatically saves the best time for the track/car combination, complete with date and session name (if done online). It's visibile at the bottom on the window, you can turn it on in the settings.
and this seems to be exactly what I wanted and more. I wish I'd known this existed earlier as it would be great to have tracked my best times and total mileage from the start.