I have a guy right now with I think 45 stamina and he rarely goes beyond 6 innings. Now, part of that is his high stuff and poor control, resulting in a lot of Ks and BBs, but his pitch count never gets above 100. Actually, even my guys with 60+ stamina are rarely allowed to get that high, but my game may have the hook a bit aggressive since my bullpen is excellent.
I once tried to convert a reliever to a starter who had everything he should have needed to succeed -- high stuff, good movement, good control, four good pitches -- except for 35 stamina. He was nearly unhittable as a closer, and mediocre at best as a starter. I appreciated getting more innings out of him by starting but it was a waste of his talents and I had to change him back. Even though IRL this guy was a starter in the minors.
In real baseball it is when the starter gets tired that he starts to get hit, and I'm sure they modeled that here too. With low stamina, that's going to happen in the middle innings, making good outings relatively uncommon and taxing the bullpen.
Pedro Martinez wasn't a workhorse, but in his mid-20s he pitched 190 to 240 innings a year. You aren't going to come anywhere close to that with a 40 stamina starter, unless you pitch him until his arm falls off.
What are this guy's current and potential stuff, movement and control? Pitches?