The hardest part of the conversation is hearing Pema say that, since it'll sound as though she's surrendering herself to death. At this point, no matter his optimism, no one would understand her own mortality than Pema right now, so he can't bear to lie to her and say they're close to some kind of breakthrough. Katara was his last card to play as far as keeping her stable, and even she couldn't find a way to counter this problem. 

I'm glad you never have a complaint. I just need to keep it that way.