The magazine was called Frequent Flyer and it lived for about 15 years. It was much more useful than Inside Flyer because it had sections in the back which broke down all new services (air, hotel, rental car, even airport improvements) by region.
I actually miss it and although I have continued my OAG Pocket Flight Guide subscription mostly from habit (20+ years will produce this sort of habit), I no longer carry it in my briefcase and am contemplating cutting the cord at the next expiration. There are just too many sources now at our disposal for this kind of information and I really don't need another book just sitting on my desk.