What plant is this?


History:
I got this plant as a gift. When I first got it, it had lots of pink leaves. The plant almost died when I first got it -- all the leaves died and fell off. I left it alone for a long time, and finally noticed that new leaves sprouted from the stems. Now, however, it has much fewer leaves and they are almost completely green. Only a few leaves have a bit of pink along the edges.
Confusion:
Once I stopped watering it, it came back to life! I thought plants like this one need frequent watering. Can anyone identify this plant so I can read up on its proper care?