1998 Honda Civic Stalling problem

My car stalls periodically; no set pattern - once, twice a week, sometimes only once a week. I have replaced the battery, had a tune-up and have regular oil changes. I was recently told that I need a catalytic converter, but was also told not to worry about it until I go for emissions testing. Why does the catalytic converter fail and could it have anything to do with the stalling problem? My mechanic cannot find anything else wrong with my car.