In some countries you can live there forever just by leaving the country when your entry stamp or tourist visa expires, then making a 'visa run' across the border and either getting a new visa or brand new entry stamp. Can yu do this in Mexico?

I think I got 90 days the last time I entered, but I'm not sure. If I don't qualify for the retirement visa, can I just enter and leave over and over? And do I need a residency permit of some sort to rent an apartment?