There are several different ways to do this, but one of the simplest is just to plug anything at all which communicates with smartthings into that outlet and then use the community – created “simple device viewer” Smart app to notify you when that particular device is no longer responding.
I believe @a4refillpad uses that smartapp for this purpose, and might be able to say more.
And here’s the thread for the smart app if you decide you want to use it.
There are some Beeper alarm devices which are not networked, but you might be able to pick up their alarm with a Leeo acoustic sensor and then have the Leeo notify SmartThings through IFTTT. Quite a few people are doing that for existing smoke alarms or water leak alarms. The problem is the Leeo itself requires mains power so it would have to be plugged in on a different circuit than the one that keeps going out. So that may not be practical for your particular use case.
People used to do this with the first generation of the SmartThings motion sensor, because it would switch itself over to battery when the mains power failed, and you could capture that event. Unfortunately, that device is no longer made.
There is a new nightlight from Centralite which has a similar feature, but I don’t know if anyone has created a custom device type handler for it and it keeps going out of stock. So that one may be a good choice once it’s in full production, but that might not be for a few months.
https://www.amazon.com/Centralite-3-Series-Night-Light/dp/B01G82NWBW
Personally, I would look at the simple device Viewer smartapp approach first. It’s more setup than just plugging in a device, but it’s available now, it works well, and it has a lot of flexibility in terms of the different features you can use. 