You have have been working with a prospective customer that is very unhappy with their current vendor.
They indicate they are very keen to switch across to your startup.
Is the sale now in the bag?
If your customer is small or has a simple decision process, it shouls be easier for them to change.
Compare this with romantic relationships. Many couples usually “slide” for big decisions such as moving in together or buying a house.
However when one partner decides to leave the relationship, that is a Big Change!
The following relationship article talks about the comparison between sliding and deciding. https://couplestherapyinc.com/relationship-transitions/
Even if they hate the incumbent vendor, it will be less disruptive to stay than to switch across to you!
My advice is to work the sales process as hard as you can until the contract has been signed! Breaking up a relationship is more traumatic than starting a new one.