To understand how far the U.S. auto business has been reaching for new customers, consider the early performance of a bond issue called Skopos Auto Receivables Trust 2015-2.

The bonds were built out of subprime auto loans and sold in November. Through February, about 12% of the underlying loans were at least 30 days past due and one-third of those were more than 60 days delinquent. In another 2.6% of loans, borrowers had filed for bankruptcy or the vehicles had been repossessed.

Those borrowers are at the outer fringe of the auto market. Still, the high level of missed payments for loans made so recently could be a warning sign for an industry that needs every customer it can get to keep sales increasing at a record pace.

The early delinquency rates seen in the debt issue from Skopos Financial LLC, a Dallas-based lender that specializes in loans to people with weak or no credit histories, are in line with those for several similar bond deals from other lenders around the same time. About 12% of the loans backing bonds sold in November by Exeter Finance Corp., another Dallas-based subprime lender, were more than 30 days delinquent through February, according to the company. A spokeswoman said delinquency rates came down from the previous month.

Loan payments have been slipping as well for the broader group of subprime borrowers who make up a big slice of the auto market. The 60-plus day delinquency rate among subprime car loans that have been packaged into bonds over the past five years climbed to 5.16% in February, according to Fitch Ratings, the highest level in nearly two decades. The rate of missed payments is higher for loans made in more recent years, a reflection of more liberal credit standards and the larger number of deals from lenders serving less creditworthy customers, according to Standard & Poor’s Ratings Services.

“What’s driving record auto sales is not the economy, but record auto lending,” said Ben Weinger, who runs hedge fund 3-Sigma Value LP in New York and who has bearish bets on some auto lenders. He said demand for auto debt has pushed lenders to systematically loosen underwriting standards, which he predicts will result in higher loan delinquencies.

An expanded version of this report appears at WSJ.com.