Headphone jack port stopped working after opening Audacity

I found a workaround that I described in the bug report mentioned in the other answer (bug 1257956, related to bug 1018262).

I went into Audacity and changed the microphone source in the drop-down menu from "sysdefault: Headphone Mic:0" to "sysdefault: Internal Mic:0" and it fixed it. I can now use my headphones, even when I restart Audacity.