SiteProbeQt is a program to monitor your websites, or other websites, and to log their up/down times.

Add a list of sites, then click Start Monitoring and minimize the program. Each event is logged
After a long time, you can view the log from the File menu.

The log lines are formatted as CSV so that you can process them using spreadsheets.
A Log line is added each time the program is stopped and started.
The program will not restart when the system reboots. Perhaps I’ll investigate this enhancement in the future.
You can find the program here: https://sourceforge.net/projects/siteprobeqt/
A Windows Installer, and the sources are available. The program should be easily portable to the Mac, or Linux since it uses the Qt framework.
Enjoy,
Windy