I'd tell this client I won't work with them any more. If they are willing to switch from the other agent in your office to you, they are just as likely to switch from you to another agent. They've already demonstrated their fickleness, which they revealed AFTER you had invested time with them instead of giving you the facts up front.
Many, many buyers believe that the market is cheap and they should be buying quality properties for pennies on the dollar. When they can't find the deal they want, they blame their agent and jump to another one. I'd prefer to work with clients who can remain as loyal to me as I am to them.