The key here is patience.
View all “lost” deals as just leads with a long sales cycle, and slowly but carefully do a specialized lead nurturing program for them.
It may take years. Just because you are “better” than your competitor doesn’t mean the customer is going to go to the effort to make the change. In fact, in the short term, that’s highly unlikely. But eventually. If the NPS is low. The customer is unhappy. Maybe in 18 months, or 2 years, or even 3 years … they’ll be willing to actually make a change.
When you are bigger, it can also even make sense to assign a rep or two here, with specialized comp plans.
And pounce — politely — when a customer stumbles. When the CEO leaves. When problems come up. This is a good time to have a conversation.