With Leah I took it off for baths or swimming but the clasp broke after about 6 months. They replaced it fine but with a longer one so I ended up giving it to a friend with a bigger baby.
Joels has been on since 3.5months, never come off at all. I was talking to a lady who sells them the other day and she said most people leave them on for baths now.
I made sure when I bought Joels one that it was the shortest length I could get and he never touches it or plays with it.