Any ideas on what caused my engine failure?
The most likely cause of your engine cutout is what's known as a rich cut caused by coarse application of full throttle. Most carburetors have an accelerator pump which jets extra fuel when the throttle is pushed in quickly, this is to make sure the engine has enough fuel and prevent what's known as a lean cut. However, at high density altitude your mixture needs to be leaner than at sea level, so it can in some circumstances do the opposite and give your engine too much fuel to burn.
It's also possible your mixture was too lean, so advancing the throttle caused it to die on you. There's no way to know for certain.
In the future advance the throttle smoothly, it doesn't have to be super slow, just don't jam it in. 2-3 seconds from idle to full is about right (same goes the other way too). If it starts going gluk gluk gluk on you enrich the mixture a couple of turns and see if that resolves it. Don't forget on a touch and go you have the option to abort, don't be afraid to use it if there's issues. Remember that takeoffs are optional, landings are mandatory.
And remember that carb heat! Icing can happen in any conditions.