Are self-healing database-centric multitier services utopia or just a hard puzzle? We argue for the latter and aim to identify the missing pieces of this puzzle. We advocate robust and scalable learning-based approaches to self-healing that we expect to work well for a large class of multitier services. We identify performance-availability problems (PAPs) as the most relevant target for self-healing, and argue that PAPs are best addressed macroscopically, outside the realm of individual tiers. Finally, we lay out a research agenda for learning-based approaches to self-healing, to enable wider deployment of self-healing multi-tier services.