If you do, be prepared with a copy of the original, which you should present to the nearest federal Migración (Immigration) office (on duty at Oaxaca City [1], Puerto Escondido [2], and Huatulco [3] airports) and ask for a duplicate tourist permit. Lacking this, you might present some alternate proof of your date of arrival in Mexico, such as a stamped passport or airline ticket. Savvy travelers carry copies of their tourist cards while leaving the original safe in their hotel rooms.
Links:
[1] http://www.moon.com/destinations/oaxaca/oaxaca-city
[2] http://www.moon.com/destinations/oaxaca/pacific-resorts/puerto-escondido
[3] http://www.moon.com/destinations/oaxaca/pacific-resorts/bahias-de-huatulco