Yes, there is. You should tell customers to go away when they cost you more than they earn you. Costs come in many forms, both monetary and emotional. If dealing with specific complaining users damages team morale, then perhaps the company should consider whether those few users are worth it.

Further, I doubt very much that bad PR like this affects Tumblr. 1) The vast majority of Tumblr users will never hear about this, 2) The ones that do will probably decide whether to continue using the service based on whether or not Tumblr actually solves their downtime problems on an ongoing basis.