The law does exist and the law doesn't exist. There appears to be no law providing "The manufacturer must provide replacement parts for x years . . .". Practicality dictates a different circumstance.
We get warranties with our cars. Mine is 3/36 + lifetime power train. Federal law and state law provide remedies for breach of warranty (over, above, and different than lemon laws). Remedies include revocation of acceptance, damages, possibly specific performance, etc. Revocation of acceptance mandated a refund.
A manufacturer would be insane to fail to support its vehicle with replacement parts for less than the warranty period. Toyota, for example, was required to repurchase a car due to a mere shortage and delay of head gaskets. See Royster v. Toyota Motor Sales, U.S.A., 92 Ohio St. 3d 327 (Ohio 2001). Porsche got dinged a decade out on failing to support on extended warranties with available replacement parts. See PFM Air, Inc. v. Dr.Ing.Hc.F.Porsche A.G., 2008 U.S. Dist. LEXIS 57405 (M.D. Fla. July 9, 2008). Under the federal Magnuson Moss Act, once the manufacturer provides an express warranty, the implied warranty of merchantability cannot be excluded. In addition to the foregoing cases, I think an argument could be made that replacement part support for at least seven or ten years is part of the "merchantable" part of a vehicle purchase (the product must be such that it would pass without objection in the trade).

So the law provides a duty to support the product with replacement parts. The end date of this duty is either merchantability viewed from the purchase date or the run of the warranty, whichever is later. Of course, all of this only buys you a law suit not a new bumper.

The foregoing is my opinion and is not intended as legal advise. The research is topical, and any reliance is at the reader's risk. No warranty is made to the correctness of the information, and gratis binding opinion letters are never provided by the author.