Ugh, I have been in a similar situation with my difficult child. The harder I tried to convince him not to be all gloom and doom about it, the more entrenched he became in his position that no one understood how HARD it was. Not sure if he was looking for sympathy or praise or just venting or giving me a heads up he was going to quit, but it seemed like nothing I said really made a difference. So since it didn't make a difference anyway I just started doing like you said, keep it encouraging and supportive. If he gets into a pity play I just don't respond.
But it IS SO hard to take.