You need wrist strength, because usually when you pop your arm is when you are trying to brace your wrist and arm straight. Always keep a little flex in your elbow and wrist, otherwise you're pushing your arm right into the path of the string.
I used to shoot regularly. Had an absolutely lovely English longbow, and a very nice laminated wood recurve. I sold them both off about seven years back... just didn't have the time to put them to use, so they went to someone who would. Honestly, my favorites are the short Turkish horse bows. Those are a lot of fun.