We have had similar problems at my job, except we have no customer support team; it's in the contracts that the customer has second line support in place and the maintenance agreement covers third line support only. But... that still doesn't help because our product is complicated and our customers aren't always very good at figuring out issues on their own.
The way we have dealt with this, is that we have split off an engineer from the development team, who only handles customer support issues, and takes other issues only when the development team is otherwise swamped and there's no customers to support. Or, if management/business decides that it is acceptable to have customers wait while the customer support guy pitches in on the major development effort. That's a management decision because they have to prepare sales reps for customers complaining about slow or inadequate service.
The upside to this, is that all of the engineers who are sprinting get to focus entirely on their sprint and nothing else, so they all become more productive; if something slips, it's not because they're distracted by other customers.
The downside to this is that the customer support guy can easily end up out of the loop on where the development effort is going, and cut out of major decisions that really need the entire team's input. The other problem is that you need a person who understands the product well enough to investigate and fix the "novel live issues" as you put it. That's generally going to be one of your more knowledgeable and skilled people, so your development team is going to lose the benefit of that person's experience during development.
Another answer suggested having a rotating roster performing this role instead of having a dedicated single person. We haven't done that here, but I think that is a good idea if you can manage it, because doing customer support like this for too long can become extremely demoralizing. There isn't the same feeling of accomplishment by completing development tasks, and it's also easy to feel alienated from the rest of the team when they're all working on YourProduct v3.2.5 with all the fancy new technologies and you are stuck supporting all of the people who are still on YourProduct v1.23.4 that still uses the old garbage tech everyone should have stopped using 5 years ago.