This should not come as a super shocking, mind blowing, surprise to anyone. As long as the 3DS is on your progress in the Ambassador NES games, lets say Metroid, will be saved on the 3DS.  Even if you  switch away from Metriod, to play another game, your progress will be saved and easily resumed. Once the 3DS goes off, or more likely the battery dies, your progress in the games will be lost.

Update: I was looking through some comments and found a problem with what I found out. One person said they turned their 3DS off and started back up again and the game was still able to resume. I found this to be true. What I did early was press the home screen button to switch in-between game, which shut down the previous game to start the other one, then I turned off the system, which reset all game data. Doing this way I was able to switch in-between games without losing my saved file. Once I turned off the 3DS the saved files were reset. If you turn off the game by pressing Home button, then the X button, which closes the game, then you can turn off the system without losing your game data.

While the 3DS is on you can switch between multiple games with out the game data being reset. Long story short, make sure you press the X button before you switch games.

Update:

I am still getting reports that some people can close out their NES games the first way I described. I did it again and I still lost my information. The only way for me to do it is the second way I described. It probably is wise to close the games with the X to make sure.