The FAQ entry for Beat Cop and Beat Cop and the old comment from 4 years ago below are kind of misleading. I believed for a long time that Beat Cop could only trigger his ability 2 times. In fact he can do it 3 times, because, as it was pointed out to me, when the cost is paid the ability is not interrupted, even if the card leaves play due to being defeated by damage. As stated in the rules:
"If the ability being initiated is on an in-play card, the sequence does not stop from completing if that card leaves play during the sequence".
The FAQ entry refers to the situation when lethal damage from enemy attack/treachery is assigned to Beat Cop. in that case there is no window to trigger ability. The FAQ entry does not apply to the situation, when a player deliberately uses ability.
So Beat Cop is even better for me now:)