Hello, if you complete a stage with a shield, you'll carry it over (except into Final Fight). It's an intended feature added with version 1.06 when I upgraded the save system.
Compared to Sonic 3 & Knuckles this game has lower chances to get a shield, so this was added to reward good play and offset the lowered shield chance a little.
At the moment there is a bug between Rusty Ruin 1 and Rusty Ruin 2 and in that case the shield doesn't carry over. It will be fixed when 1.10 hits.