Why does my kitchen faucet's hot water line rattle and lose pressure?
If you're only opening it just a bit, then it can be thermal expansion.  When the hot water reaches the valve, it can cause some component to lengthen slightly, closing the valve a bit more than it was.  

I've seen that exact behavior on bathtub valves as well.  If the behavior is new, it could be that a washer is staying compressed when cold and is expanding only when it gets warm.  If so, replacing the washer may change it up.

Does it cut back 50% if you open the valve all the way, or only if you open it a "normal" amount?