Pretty sure this has to do with the fact that isWet() is employed instead of isInWater(), making it so certain activities will make you stop jumping. Also, the motionY check seems redundant, so I changed the update() function as follows:

@Override
public void update(EntityLivingBase target)
{
    boolean moving = target.moveStrafing != 0 || target.moveForward != 0;

    if (target.onGround && moving && !target.isInWater())
    {
        target.motionY += 0.5D;
    }
}

This makes it work as intended, at least on my end.

Would you mind pull requesting that?