IP Host Monitor Free

You can track up to 4 IP adresses. In setting you can:

Set IP addresses
Set Phone notification
Set Mail notification. Email address is preset.
Read records about outages in recorded history
Clear whole setup and recorded data.

Limit to recognize dead IP address is 25 seconds to avoid micro outages.
When IP will be available again you will also get notification.
Application is not supposed to run in background so just plug the charger, keep it running and enjoy notifications.