Absolutely. I came from Asia country where the time is one day faster than U.S. I can always maintain connection with my family and friends back home through Facebook, BBM, email, telephone, and Skype. Thanks to the high-tech!
If by "connections" you just mean friendships or relationships, then of course! However difficult maintaining connections in our lives gets, having strong friendships are really important to the growth of a person; having another to struggle through difficulties with you and celebrate the triumphs.
As for relationships with people, I definitely keep in touch with them. There are so many ways to connect with people, the internet, the cellphone, webcamming, ect. You can even reach people in the random jungles of Asia with the internet. It's freaking amazing.