“We're locked into a contract with our current provider.”
Why they say it. It is a legitimate timing and cost barrier, but it is also a convenient reason to defer the whole conversation. Often the contract end is closer than they make it sound.
Do not: Do not walk away until renewal, which surrenders all influence over the eventual decision.
That is fair, and I would never tell you to eat a contract you are committed to. The smart move is to use the runway, the teams that switch cleanly start the evaluation months before renewal, not the week of, so they are not making a rushed call under pressure. When does that contract come up, and would it be worth lining up a real comparison before then so you have leverage?
Then ask. If you were free of that contract tomorrow, would you stay with them or would you be looking, honestly?