I'm not sure what type of plant that is, but from the look of it, you need to check a couple of things out. One is to check and see if those rocks are glued on. Home Depot and other similar stores take a random plant, strip a few leaves off and call it a bonsai. A bonsai is supposed to represent and old, old version of the tree you are growing. This includes a tapering of the trunk, drooping branches from years of snow loads, etc... most of these plants don't have that.
Regardless of that fact, what I've seen is that they prep these plants somewhere and to keep them looking pretty, they glue the rock in place to keep them from moving in shipping. The glue prevents the rocks from moving, but also prevents water from penetrating, which could be why it's loosing leaves. You'll probably also find that they put regular potting soil under the rocks, which is not appropriate for bonsai.
You can look online and find many recipes for bonsai soil and how to wire and shape them. Chances are, you could probably turn this into a real bonsai. What you'll find with the soils is that they are mostly inorganic rock-like material. The more organics you have, the more water it retains, but it's not good for the plant. However, the less you have, the more you have to water. So it's about finding a balance for the weather you have in your area. Basically, you want to put a chop stick in the "soil" and leave it in there for about 15min. If you pull it out and it's dry, you need to water. Water from the top down, soaking the leaves and water till it runs out the bottom of the pot. About once a month, during the growing season, water it with 1/4-1/2 strength balances miracle grow fertilizer, or you can buy a bonsai fertilizer. And like some of the other posters stated, most bonsai need to be outside as much as possible or they won't survive. My juniper bonsai needs to be out in the full sun and needs the cold of winter to do well.