My villagers are not getting any older! I have had the game on for about a week straight constantly running. Two of my key villagers became weak and died. I have 2 babies that have not aged and have been stuck on being nursed for 120 minutes. And both of my children are still 4. After a week shouldn't something have happened??

Have you, perhaps, adjusted your computer's system clock since starting to play the game?

will that make them grow older?

Not having good medicene can.

Could daylight savings be responsible for this?

It's possible, if the system clock was adjusted while playing the game, or in such a way as to create a situation where the game detected a backwards movement of time. Normally, the semi-annual time change isn't a problem for the game if the game isn't running at the time. You can read more about it in this thread.