Nope - been doing it for years with my Mexican plated vehicle (purchased here). I still have "Residency" status and a valid Canadian driver's licence but prefer to use my Jalisco driver's licence. This way, you don't need to worry about getting or paying any tickets you may receive as a result of a traffic violation in Canada. Mexican driving habits acquired here tend to result in attention from the cops up there (parking in the wrong places, rolling stop signs, speeding slightly over the limits, etc.).
Christiane, I know of no law that requires you to give up your legal "residency" status in Canada when you become a permanent resident of Mexico. Whether someone holds Canadian "resident" status or elects to declare "non-resident" status has more to do with what property you still own in Canada, how long you are there in a given 12 month period and your resultant tax bracket.