Is there a word to describe someone who is always defeated at my hand?

B is A's punching bag.

B is A's whipping boy.

Stooge.

Sucker.

Schmuck.

Mark.

"Mark" and "punching bag" are the least offensive. "Mark" is the least informal.

http://thesaurus.com/browse/whipping%20boy

I think the best term depends strongly on how the conflict between A and B comes about.

If the weaker B is the instigator of the conflict despite being repeatedly defeated, they might be called a "challenger" or "contender".

On the other hand, if the stronger A is picking on B who is no threat to them, B might be described as "victim", "goat", "whipping-boy" or any number of other more offensive epithets (including, as Earnest Friedman-Hill commented, variations on "bitch").