Can you quantify the lost sales associated with not having this feature? Nothing motivates like numbers.
Does the request differentiate you or is it a market expectation that you should have it?
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Do you have a board or posting with votes for the feature request? Is it a feature for a client or a small group of clients that other clients can use or the feature has to grow and expand so more clients can use it? Depending on the sector, is it a feature that could be a Beta or in an Early Adopter program? If there are a couple of clients interested already, show your stakeholders the equivalent number in sales or recurring revenue for this group of clients.
While the reasons for stakeholders being resistant on that feature remain unclear in your description (probably for a good reason) the most obvious choices are the following: