The textbook counter to hi yoyo is to level the wings, gain speed and maintain or even increase the separation. It is possible to lower the nose a bit for a shallow dive acceleration. When he comes down from the yoyo, start to turn again. Unless he commits to a high speed, high G turn which will blow his E advantage, you can keep this up for a while. Eventually he will run out of patience or run out of energy advantage, or just make a mistake and allow the separation to grow to big or too small.
What he is doing with the yoyo is to adjust his circle with respect to yours. Most people imagine the turning circles and two overlapping circles, or two co-centric circles. This is almost never the correct picture - the circles are almost always displaced with respect to each other. When you go into a flat turn, your circle is set and very predictable. He will adjust his position and turn circle for a future interception point - destroy his extrapolation by running away and taking your circle with you. i.e., not turning. He will come out of the yoyo with his high E on your far 6 and you are back to square 1.
If he is predictable with his hi-yoyo, then start faking turns by banking and initiating a very gentle turn. When his nose go predictably up, straighten out or even initiate a gentle, nose low turn to the other direction. Many pilots will be frustrated by this, push the attack and allow you to reverse them.