In 2012, the label for Propecia was updated to include reports of adverse effects that continued after stopping the medication. Here’s the relevant part of the label:

A TIME story about the label update included comments from an FDA spokesperson (emphasis added):
“It’s important to note that these labeling changes are not new warnings, as characterized by other news reports. Sexual adverse events were reported in clinical trials, and this information was included in the finasteride drug labels at the time of approval,” says Stephanie Yao of the FDA Office of Public Affairs. In those clinical trials, the side effects resolved in patients who stopped using finasteride, as well as in most patients who continued therapy.
Alexandra Sifferlin. FDA Adds Sexual Side Effects to Propecia and Proscar Labels. TIME, April 13, 2012.
In fact, reports of adverse effects which continued after stopping the medication were added to the label for the first time in 2012. I checked the prior state of the label, dated June 9, 2011:

This 2011 label stated: “The side effects went away in men who stopped taking PROPECIA.”
An FDA letter to Merck in 2012 confirms that the agency required adding to the label reports of adverse effects that continued after discontinuing treatment:

It appears the 2012 statement from FDA Office of Public Affairs (OPA) that “these labeling changes are not new warnings” was incorrect. To confirm, for the first time in 2012, the Propecia label noted reports that three sexual adverse effects “continued after stopping the medication”:
• decrease in sex drive that continued after stopping the medication;
• problems with ejaculation that continued after stopping the medication;
• difficulty in achieving an erection that continued after stopping the medication.
FDA label for Propecia as of April 11, 2012
See also: Adverse effects in the Propecia label: a history of changes