Yes, he can, because of the way contract law works.
In order for a contract to be valid, and enforceable on both sides, there has to be an offer, acceptance, and consideration. No consideration (payment), no contract, and the open source license reverts to what is known in law as a bare license. Bare licenses can be revoked at any time, at will, by the licensor, regardless of any promises made by the licensor to respect the license in perpetuity. (You can always tell a squatter to leave your property, regardless of how permissive you've been in the past.) This includes revoking the license to software downloaded under an open source license for which the licensee has given no consideration.