A few things off the top of my head:
1. Not enough brake cable tension. This is very likely if it's fairly new and hasn't been tuned up -- brake cables stretch over time, especially when new. The amount of stretch can be more than the barrel adjuster can compensate for, so you would need to actually pull more cable through the cable clamp on the caliper.
2. Broken (or worn out) caliper spring. Less likely, but you should be able to see if it's broken, depending on the model of brake. Your LBS might also be able to replace the spring rather than buying a whole new caliper.
3. Frayed cable or housing causes cable to "catch" and not spring back. Might be harder to find, you'll need to inspect the cables and housing for damage (may need to pull the cable out completely). The good news is that these are relatively cheap & easy to replace.