Interesting response from Admin:
There's a lot at play in this logic. It turns out the fact the pitcher had a call bullpen of 1 (Very Patient) was enough to just push the decision to leave him hit for himself since there were two out and he had enough pitches remaining to go another inning and the team was down by four.
Had it been a 3-run deficit, or a runner on base, or < 2 out or Call Bullpen of 2 or higher or 9th inning, he'd have been pulled.
We tend to agree with you, though, that he probably should have been lifted. As a result, we've made a slight adjustment that will be part of the next engine update.
I wasn't aware the call bullpen settings affected pinch hit decisions -- I thought they only applied to when a pitcher was on the mound.