In the event that payment is not made by the due date on the invoice then the transaction is essentially null and void and you can sell the work to another client.
For your particular situation I would strongly suggest that you implement a sales contract and agreement of original transfer of work of art for any and all future sales of your original works of art. In this contract you need to either enforce payment in full at time of signing or a deposit at signing with payment in full within (X) amount of days and upon delivery of item.
In your sales contract you will want to stipulate a late fee in the event that the client does not pay the balance by the date specified, and a clause that stipulates how long after the due date that you will hold the artwork before the client forfeiting deposit and losing rights to the work.
You will also want to specify an amount of time that you provide as a grace period in the event client changes their mind about the purchase, and you can make it zero grace period, making all sales final and upon signing of the agreement the client agrees to the terms and is locked into the sale. In which point if they back out they forfeit all deposits paid.
I own a custom web design business and we implement a similar agreement for all works that we create for a client, requiring a 50% deposit in advance of work being started, an additional 25% at time of client accepting the design/layout and the final 25% at delivery of finished product.
In the event that a client fails to meet the requirements of the contract for the second or final installment payments the client forfeits all money paid and actually owes us 70% of total quoted project price for wasting our time. We have only had to enforce these stipulations on one client in 5 years!
The benefit to you for requiring a deposit if payment is not made in full is that it ensures that the client is serious about purchasing the work because they have put money in the game rather than just their word of wanting to purchase. Think of it like putting earnest money down when you make an offer to buy a house.
Hope this helps!