This question gets asked a lot. Daphne is just an emulator, so the game behavior is based on the roms that you are running. Daphne makes use of the F2 revision of the
Dragon's Lair roms (these were the latest US release).
At least with the US release of the game, when you died, you moved onto the next scene, but the game remembered which scenes you hadn't completed. When you reached the Dragon's Lair, any scenes that you hadn't completed would be re-played before you would be allowed to play the Dragon's Lair. If you died on one of the replays, then the scene would play again immediately until you passed it. Once you had completed all of the scenes, then you would move on to the Dragon's Lair.
The exception to this pattern was the nine-level falling platforms. If you died on one of those scenes, it would play again until you got through it.
For further details, take a look at
The DLP's Scene Sequencing Page.
Non-US releases of the game may have worked differently.
Space Ace was different. When you played
Space Ace on any skill level above Cadet, you had to repeat any given scene until you got through it without dying (on Cadet, if you died, you would continue the same scene from shortly after the point when you died).
-etumor