"So," you may be wondering, "what does the buyer have to prove in order to recover his downpayment?"
As a threshold matter, the general rule is that to recover on a breach of contract claim, the party alleging the breach must demonstrate its own performance, or ability to perform, under the contract. Or, as New York State's highest court put it well over a century ago,"The contract between the parties to the action [is] mutual, and neither [may] recover against the other for a breach of its terms, or put the other in default, without a tender of performance, or at least proof of a readiness and willingness to perform." Nelson v. Plimpton Fireproof Elevating Co., 55 N.Y. 480, 484 (1874).
Of course, there is are some "small" caveats to this rule, including the buyer's first line of attack, which will typically be that the seller failed to satisfy a condition precedent to the closing, such as an inability to convey clear title to the premises, or in the context of a co-op, that the seller failed to get board approval for the sale. See, e.g., Ismael-Aguirre v. Wharton, 27 Misc.3d 1225(A), 910 N.Y.S.2d 405 (Sup. Ct. N.Y.Cty 2010).
Naturally, it would strengthen the buyer's case significantly if he is also be able to prove via competent evidence in admissible form that he was ready, willing and able to perform his obligations under the contract of sale, which - most importantly - means having the financial means to complete the sale (and in most cases, will entail a current, valid mortgage commitment) at the date and time set forth for the closing.