Ah, okay. I was thinking of something else, my bad. On the subject of Rings, I think we should use them here, since A) it gives us an accurate health system for us to use (i.e. we know X attack takes away Y Rings), B) it doesn't cause any issues that a regular health bar wouldn't (translating damage from one game to the other would happen with a regular health bar as well), and C) it's one of his most unique attributes (not many characters have their life bar fly out of them, ready to be collected again).
As for the amount of Rings, we're giving all characters maximum ammo and health, and Rings count as both. Now, in the main gameplay, Sonic can usually hold up to 999 Rings. However, in Sonic Adventure 2, there is a mode where you can have a pet Chao, and, playing as one of the playable characters (including Sonic, of course), train it, feed it, and, most importantly for this discussion, buy it things. These things are bought in a store known as the
Black Market using Rings. The most expensive item listed in the Black Market is Maria Robotnik's Menu Voice (a skin for the game's menus), costing a whopping 30,000 Rings. Naturally, the characters (including Sonic) can hold that many Rings in order to buy the item with. And yes, the health item Rings and the currency Rings are the same thing, since the Rings collected in levels for health also carry over to the Chao Garden (as well as carrying over in other games, such as Sonic 2006 and Sonic Unleashed).
Anyway, this would allow him to stay in Super Sonic form for about eight hours and twenty minutes (not factoring in damage, of course), based on the fact that Super Sonic consumes one Ring per second. While it might not be the three days Link can stay in his Magic Armor, I'd say it's more than enough for someone of Sonic's speed to deplete his Rupee count (let alone defeat the other fighters).