I'd say no. I do remember the bad seasons of the 1970's, but I was younger then and more captivated by baseball in general. I could also laugh those seasons off back then. It helped that Jack Buck and Mike Shannon were hilarious at the ends of those seasons: They made bad baseball listenable while being brutally frank about the teams' shortcomings. I could also follow particular players like Gibson and Simmons.
I had the championship in 1982 to tide me over for a while.
I was finishing up grad school and starting my job in the late 80's through the 90's, so I wasn't following the Cardinals much then. Being in Philadelphia and Maine for several of those years meant I stopped following the team for a while.
If the Cardinals were playing really engaging young players, and there were a recognizable plan to the development of a new core of players, I would follow for two or three years, but probably check out after that. By year four or five, there's a clear problem, and I've got too many other options in my life. At my age, I'd probably check out for good.