As stated on Torah.org (as translated) by Rabbi Aaron Tendler the conclusion is:
[I]f the seller approaches the buyer and requests a new check because he had lost the previous check, the buyer has no obligation to provide the seller with a new check.
It would be proper, however, for the buyer to go Lifnim MiShuras HaDin (beyond the letter of the Halacha) and issue a new check if he is given guarantees that he will incur no loss by doing so.
Basically the idea is that since there is some possibility of loss to the check writer by writing a second check, the check writer isn't obligated to take that risk.
Given the analysis there, it relies on some assumptions about check writing and liability that seem tenuous at best given the way that banking has changed in the last 5/10 years. It can't be that the slightest and most remote chance of double cashing is a problem - there has to be some substance to the concern. Given the legal changes (in the United States anyway) the conclusion there may, or may not, hold.