Alright, I spoke to Executor about this. I'm pretty sure he was busy, so he just left a single comment. I'll do my best to try and cover all the points within his
blog, as I'm copy-pasting most of this.
"During Sonic 186 Mogul explains that somehow, Sonic is protected by a great power that prevents Sonic from being defeated. No matter what happens, it does not matter what disadvantage Sonic is in. (In this case referring to the two times that Mogul became Master Mogul) fate somehow changes to ensure Sonic wins, as some kind of cosmic joke against the enemies of Sonic." (This is coupled with the first scan below)
"Also in Sonic 187 Merlin appears to break the spells of Mogul and Finitevus, he finds curious the fact that Sonic had not been affected by any of this and wanted to make sure that nothing bad had affected him." (Second scan below)
"In Sonic 200 Dr.Eggman goes crazy after being defeated by Sonic several times, he goes insane. After 10 issues, Eggman apparently regains sanity. From time to time Eggman realizes the meaning of everything that had happened until then, because Sonic was the one that most absorbed Chaotic Energy in all his existence (which had already been confirmed by the Ancient Walkers) that ended up making him in the Embodiment of Chaos itself. Chaos itself is an invisible force, which is unpredictable at the quantum level of which no planning is capable of preparing for it. Sonic would be the chaos, the constant of inconstancy.
Basically this means that no matter the situation, there is always a minuscule possibility of something completely unpredictable happen, and as Sonic is the very embodiment of chaos, then he always had this in his own favor." (Third scan below)
"Knowing all of this, Dr. Eggman developed a project from which he could rewrite all reality, and thereby rewrite Sonic himself, taking away the power of chaos. But you know... this is a plan so..." (Fourth scan below)
"Even in this situation, Sonic's chaos constant acts and protects Sonic. In this way Eggman still needs to include the constant of chaos in his plans trying to find a way to solve the puzzle of predicting the unpredictable and unexplainable. As Sonic is still the chaotic constant he still acts against Eggman until the last second, and as he is chaos then he does the impossible. A current of energy that should kill him actually turns Sonic into Super Sonic. Because Sonic is Chaos, it's the constant." (Fifth, Sixth, and Seventh scan)
Everything here is from Executor's Archie Sonic Blog. You asked for examples and context, and sorry if this doesn't please you, but this is the best I can do. All of Sonic's unlikely victories, all of the times he shouldn't have won but did, all of it can be attributed towards his Aura. Because there's a chance for something to go wrong, reality essentially chooses that one because
it's chaos. That's how the power works. It's crappy for the story, but there you have it.
