This might be overkill, but it is pretty easy. In enterprise networks we use monitoring tools to get alerts whenever something goes down or has some other issue. One that I have used, and offers a free trial, is SNMPc. You can download and install it, then just set it up to monitor your internet connection. It will keep a log of all events that happen in the period you have it running. It will tell you motr or less exactly when it went down and when it came back up.
As you probably don't know what router your ISP ahs you connecting it to just add an instance of say the DNS server they want you to use, or google, or anything that would force it to use the internet. If it goes down, you can't reach it. A log entry will be made.