Subhash SiteChecker app can be used to monitor websites and keep track of their uptimes. Once started, the app runs in the background and monitors specified websites. If a link downtime is detected, then the app displays notifications and/or sends messages to specified e-mail recipients if required. The app is not dependent on any web service and is entirely self-contained. It is free for personal/commercial use. As with all my apps, it displays no ads and contains no nags.
Download & Installation
You will have to first enable installation of non-store apps from the Android menu:
Settings » Security » Unknown Sources or
Settings » Apps and notifications » Special access » Install other apps
You can then download and run this APK installer. After completing the installation, you should disable the above setting.