I got my Flytrap from the Natural History Museum, there were lots and lots of kids, so it may very well have been stimulated to shut a bunch before I bought it. I've had it for about 3 or 4 months, all of a sudden there are three traps wide open with flies in them and they won't close. One has a fly in it and is closed. I have it outside on my front porch on one of the stone pillars so it gets plenty of light. I water it almost every other day with purified bottled water, I keep it in a ceramic bowl and put the water in the bowl so it stays nice and moist. Any help would be appreciated. I sure have grown to love the little guy.
I think you are following the proper way of growing venus fly trap.
The first year i started to grow venus fly traps it happened the same to me, traps were lazy and they began to close very slowly, next year I repotted my plant 50% turf 50% perlite and they got better, anyway I needed another year to start to have nice plants again.
Did you try to stimulate one of the three hair inside the trap? These marvelous plants have a memory, so if you stimulate only once the trap won't close, but if you stimulate the hair a second time within 30 seconds it closes, if you stimulate again it will restart counting down to 30 seconds and wait for the second stimulation. Of course stimulation it should be made very seldom in order not to stress the plant.
Some source on Venus Fly Trap (aka Dionea Muscipula):
For me, the youngest traps snap closed the best, but the older traps become convex and seem to loose interest in feeding. I have a lot of Venus Flytraps which I grew from seed. It is fun to see the differences between seed grown plants. You said you are using "purified water". You should be using distilled water since "purified" can mean many things, for example sterilized spring water which can contain many minerals harmful to flytraps. If you want to keep your plant for more than one year you should search the web for their winter dormancy requirements since this is essential for long bug eating lives. The web has many great sites explaining how to care for your plant.