MichaelMeissner:
Yes, the bits are probably on the old-ish and probably need replacing. However, as I said, I had bought a concrete bit specifically to hang some shelves (project #823 of my undone projects) and I couldn't get it to make a hole with the new bit. So, I assume I need something with more torque. I don't know when we bought it, but I think my wife bought it primarily as a power screwdriver.
Concrete can be quite difficult. I don't remember that I've ever drilled into it with a plain old drill. It really takes a rotary hammer (hammerdrill), and even then, I've come across some concrete which was very hard, and gone through multiple bits. If you look at a masonry bit, you see that the end isn't a cutting edge, it's more like a broad v-shaped chisel. The intent of that is to break the concrete (or mortar, or brick). Just spinning it will get you almost nowhere, unless you're drilling into something softer, like plaster, or maybe some brick or mortar. I used to have one of these. That was the shizznit! Works as a regular drill too. There are smaller versions from various makers available. Even cordless.