EverWatch Server Monitor Description:

EverWatch Server Monitor allows you to continuously and automatically poll the web server of your choice at a specified interval. Check your web host to see if it's really up as much as they say it is. Detailed event and statistics logging can optionally be saved to file. Easy to install, configure and run.

Runs in background in system tray. An always-on internet connection is recommended for continuous polling, but not required for occasional monitoring.