I play on Hard a ton, and I’m actually leveling up my P3 Alarak 
.
However, I don’t have my partners leave usually. Granted, I play on Void Thrashing most of the time, to get the bonus “First Win Of The Day”.
When people are leaving at the start of the map frequently, I’d suggest asking on a discord co-op server, or the co-op chat in-game for a match.