Having to sacrifice your own Pokemon to win.
I have a handful of examples, but the one that arguably hurts the most was from my recent
Fire Red Omega Nuzlocke, where I lost Oscar the Gardevoir to Sabrina's dreaded Alakazam.
Let me explain. Beatrice went up against Espeon at a severe disadvantage on low health and being paralysed, so after paralysing Espeon and healing poor Beatrice, she was set to take down the lavender cat. Until the Espeon - after setting up plenty of Calm Minds - used Baton Pass to Alakazam. At that point, my run was on make-or-break mode, as I had no other choice but to send in Oscar.
Although he took a near fatal blow, Oscar managed to hypnotise the Alakazam into falling asleep. As I was contemplating on what to do, there was one option that would give me the best chance to beat Sabrina. Healing Franklin and Beatrice. So after spending three turns in healing the duo, Sabrina's Alakazam finally woke up and killed Oscar.
While the run is completed and history now, I still feel gutted in losing Oscar in that situation. While he became a counterpart to Franklin when he learned Ice Punch (keep in mind, this is
Fire Red Omega), he was still a valuable member to the team who would've been beneficial towards the end of the run. Yes, Sabrina is one of the most feared Gym Leaders notwithstanding
Omega, but I was very lucky to walk away against her with the run to be continuing at that point.