In five years in Mexico, never been asked for my DL by anyone other than the Banjercito while getting a TVIP. My wife did get pulled over by a MC traffic cop in Hermosillo. The DL was only used as a device to obscure the mordida being handed over. The DL was handed right back less the 20 peso note.
I suggest following the advice on reporting your DL lost and getting a replacement issued. Failing that, just make a really good copy of both sides and laminate it. You can also find fake DL's on the web but they might cost more than a real 2nd license.