If you do, present your passport at the police station and get an official police report detailing your loss. Take the report to the nearest federal migración office (at the Puerto Vallarta, Manzanillo, and Guadalajara airports) or oficina de turismo (in Puerto Vallarta, Guadalajara, Tepic, San Blas, Rincón de Guayabitos, and Barra de Navidad) and ask for a duplicate tourist card. Savvy travelers carry copies of their passports, tourist cards, car permits, and Mexican auto-insurance policies, while leaving the originals in a hotel safe-deposit box.
For more complicated cases, get your tourist card early enough to allow you to consider the options. Tourist cards can be issued for multiple entries and a maximum validity of 180 days; photos are often required. If you don’t request multiple entry or the maximum (el máximo) time, your card will probably be stamped single entry, valid for some shorter period, such as 90 days. If you are not sure how long you’ll stay in Mexico, request the maximum (180 days is the absolute maximum for a tourist card; long-term foreign residents routinely make semiannual “border runs” for new tourist cards).