I have faced many such instances in the past. 😃 I will share the one that happened earlier this week.
So, we migrated our old AMAs into traditional thread based system. After deploying the change, we observed slow response times of our APIs and the website slowed down significantly when @unclebobmartin announced his AMA.
Server logs didn't reveal anything and it was too frustrating. After a couple of hours of debugging and tinkering with newrelic, I realised that I had missed a DB index which was leading to slow queries in peak hours. After migrating the old data, I was supposed to index the amaDate field. That was a huge bummer! :D