The rings are always present on his wrists throughout the entire game. They are a defining feature of his design and serve as a visual reminder of his connection to the Master Emerald.
Perhaps you are remembering something else from the game?
It is possible you might be thinking about the rings on his gloves, which do disappear during the game's ending cutscene. However, this isn't necessarily a deliberate act.
* The rings on his gloves are simply a design choice, not an essential part of his character or powers. Their absence at the end of the game isn't significant and doesn't hold any deeper meaning.
If you have another detail about the game you're remembering, please let me know!