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.