It's probably fine. Are you sure it's closing by itself? Or maybe it's opening.

No, I think it's an older trap, one of the smaller ones near the bottom. It looks more closed than when I got it, and I read that sometimes a trap ends up dying. But this could be from it putting on new growth, perhaps. Oh well, the plant itself seems to be very healthy. Thank you for your reply.

Flytrap's traps will eventually lose their ability to function as a trap. They can only open and close a certain number of times. Don't worry, this is perfectly natural and new traps will grow and replace the older ones. Just leave the old traps as they are, they will still continue to photosynthesize and provide energy to your plant. Or, if the trap has died back, then just pinch them off and leave the rest of the leaf to provide energy as well. Once the whole leaf has died back, you can trim all of it away. Just make sure to wait until it's completely died back before removing it. So your flytrap can reabsorb any reusable nutrients back, to use elsewhere within your plant. :)

Yeah, the trap hasn't closed any more since I first posted. I did have to remove a few of them after it shipped, since they had started turning black; I figured that such an effect was most likely due to the plant being in a dark box with a dome over it for a few days. At any rate, there are quite a few little stalks starting to come up, so hopefully in a few weeks it will have even more traps.