A number of times I've noticed that when a mob dies, it's corpse appears to cover up any trap that it appears to be standing on. I suppose it's possible that I may have mis-clicked and disarmed the trap, but I'm pretty sure that I didn't.
I thought traps went away when they were set off. If a monster stepped on it, the trap should be gone.
Most traps do go away after one press. There are a few that state they're good for X amount of activations. The arrow ones stay until you disarm them though.