As a get around, perhaps open an .app at startup that logs time, as for client billing.
One which adds time each session.
There may even be one with OSX, I don't use them myself.
Search for "track time" in Macupdate, it shows a few free ones.
examples include
Time Tracker 1.2.5
TheDailyGrind 2.0.2
Active Timer 1.3.3
or a stopwatch that auto increments each time you switch on ?
or ....
have an app that does something every hour for example, that will also create a log by time !
or 2 ... create a new folder at power up, and again before power down.
Collating these will show RT