We've started doing the same thing for major customer issues. While the issue is going on, just get through it - you're wabbit hunting! But once the issue is resolved and the customer is back up and running, consider having a postmortem.
Just like you can build software better, faster, more reliably, you can solve your customers problems better, faster, more smoothly. So get the team together - support, development, the account rep, and maybe even the customer - and see what you can learn. Questions to consider:
- What could have prevented this from happening in the first place?
- What is the customer's perception of how this issue was handled? Were they pleased? What would have made them more pleased with your handling?
- What changes should be made in the product or in procedures that would have enabled earlier detection of the problem? More precise detection?
- Could this problem have been caught internally? If so, what can we change to catch these types of problems before they get to a customer?
- How disruptive was this issue internally? Is there anything we can do to reduce that?
- What is the "signature" of this problem? How will we recognize it if we see it again?
Not every issue needs a postmortem, but for the large customer problems, pausing after it's over to think about how to make it better next time can certainly prevent future headaches.