RE: first flight good, second flight BAD.
Well i remember this problem well from my days of pylon racing many years ago. Everyone racing would always try to get a few extra RPMs on the top end by tweaking the needle valve. If you went a hair too lean, the engine would lean out too much part way through the race on you. So you had to develop a feel and touch for how lean you could go without going too far. Later in the day when the temperatures changed the needle valve settings would change. Everything could affect your engine when racing as well, not just the temperature, but humidity and barometric pressure too. Some guys would change out to different glow plugs depending on the conditons changing during the day. Even the nitro percentage in their fuel could change during the day too (if you didn't have to use the club fuel for racing). the propeller used could change too.
Everyone kept a notebook or log of everything they did too.
Anyway I would still suggest that the OP have his friend run the engines on the rich side. Find the peak RPM setting and back it off about 500 to 1000 RPMs off of peak. Some engines have better fuel draw than others to. Then after it starts to work OK, then lean it out a little more, but careful. Point the nose of the plane to the sky and adjust the needle at WOT and back it off a little from peak, say 500 RPMs. Then the plane should work fine.
On really hot and humid days the engines can really lose a lot of power and you have to run them even more rich to prevent them from overheating or detonating even. You just have to live with the lack of power in these cases. I remember a few days where I would show up early and when it was cooler get in a few flights no problem. But then others would show up, and I'd help some guys out and later when it heated up more, I would find my engines were too lean now and needed to be richened up a little, before I could fly the planes again.