Excuse me for lacking the needed descriptions. Let me try and clear some things up:
The problem is with the cranks, not the BB. The become loose axially (so long as that's the right word to describe movement perpendicular to the bicycle). And I need to re-tighten the bolt because it works loose.
The cranks are two weeks old. They were new when I got them. I also think it's too early to think that the cranks are broken. Forget getting new cranks for now: I'm going to take these to the LBS before I decide I need new ones. Also, I see operator's point, and that a different interface won't fix the problem. (I wasn't thinking about my problem much when I said that.)
But, for reference for the future: what can I do myself?
When installing my cranks, I did grease them. I know some people say to not grease square-taper interface, but I think that's ridiculous, especially after reading a
particular article on Sheldon Brown's website. I use a ratchet, though it's not an 18" (as suggested by DannoXYZ). I haven't much experience with tightening things to a measured torque, so the best description I can give is, "I tightened them 'thoroughly.'" I intend on getting a torque wrench for my personal bicycle-repair in the future because of this incident.