Is there a way to stop time?

You can't stop the movement of time, but you can set the 3DS system clock to shortly after you last played.

This will trick the game into thinking that you haven't been gone for a long time, but you'll have to keep track of when the last time you played was, according to the system clock. If you don't remember what date it was, you can always browse through the Activity Log. Be careful when changing the system clock, though, as this may have unintended consequences for other games that use it, including the Activity Log itself.

Alternatively, you can change the game clock. This will avoid any interactions with other games, but will cause the player to randomly trip for approximately one day after the change. You can read more information on the consequences of changing the game clock in this answer.

The major consequences of long absences are that weeds will appear around your town, and one of your villagers will likely move away. Flowers may also wilt and die, but this does not appear to be any worse after being gone for a long duration than it is after being gone for 2 or 3 days. You can greatly lessen the number of weeds that appear and keep the flowers alive be enacting the Beautiful Town Ordinance. This will also prevent cockroaches from appearing in your home. If you don't mind losing a random villager with each prolonged absence, I recommend using this ordinance and leaving the system clock alone.

With the DS version, I believe that there is a in-game clock that you can set to the last time you played. The villagers may not be the same but the number of weeds are reduced drastically.

When you boot the game and Isabelle greets you. You can tell her you want to "do something else". One of the options is to update the time. As long as you do not roll the time back to before the last time you played you will not suffer any negative consequences. So if you want to do this, you'll need to keep a log of the in-game date and time you last played. Then the next time you play readjust the time accordingly.

Here is an example for if you want to play consecutive days (in-game time) in the game.

A) If the real time was

B) the game thinks it's

C) and game time is

A) Feb 26, 2015 : 6pm

B) Feb 26, 2015 : 6pm

C) Feb 26, 2015 : 6pm

the next time you play change the game time

A) Feb 28, 2015 : 11pm

B) Feb 28, 2015 : 11pm

B) Feb 27, 2015 : 11am

then...

A) March 4, 2015 : 4pm

B) March 3, 2015 : 4am

C) Feb 28, 2015 : 11am

and...

A) March 10, 2015 : 4pm

B) March 7, 2015 : 9pm

C) March 1, 2015 : (whatever time...)

etc...

If you ever catch the time up with reality just roll the clock forward to the correct time and you're done. If the date forward range crosses more than a week you'll usually trigger time travel penalties though.

If you ever roll your time back to before a time that has already passed (even moving time back 1 minute before the last time you were playing in the world) then you trigger any time travel penalties as well.

I hope this helps clear this up.