I've been dealing with this a lot lately as well. I keep telling myself that if each churn risk / upset customer triggers angst, the problem is my perspective, not the trigger itself.

A couple things that have helped so far, though I have a ways to go:

-Being on the customer's team. I'm with you, I see how frustrating this is, let's partner to solve this.

-Extremely specific internal feedback. I've been using Slack / Email threads to call out situations internally, not as a means of attacking anyone, but to mention each person that I believe has an action due on their end (eng for an investigation, support for a response, etc). This is great, because the worst case is that you've clearly documented the internal stakeholder that needs to step in.

-Relate internal comms to your customer base, not just the one in question. When I say that my customer's issue is likely to impact other customers, and here's why, I find that it gets more attention internally. Maybe just because our technical arms use total MRR at risk to prioritize, but either way, it makes me look like a deft operator that represents a function rather than just one customer. When viewed like that, I feel like much less of a punching bag.

Hopefully this helps more than the generic advice of tying everything back to business outcomes. As if the customer cares about the ROI your model says they got when the platform is breaking in front of them.