Here is a special version of GarageSale, that generates a log message each time the scheduler runs. Please download and install it:
Once you have it running, please open the Console utility from (/Applications/Utility), select system.log and use the search field in the top right to filter for GarageSale (as shown on the screenshot).
You should see a new entry “schedulerTimerFired:” around every 30 seconds.
If you leave GarageSale and Console running, do you see log messages around the time your listings are supposed to go online?