If you have kids in school, you're going to get the flu every year or two.
I'm not quite so extreme, but I do avoid flu shots about one out of every three years for the same reason. In any case, I don't get the flu very often.
Unless you mean that the upper respiratory tract inflammation itself is what would cause the beneficial effect?
But from then on, while you certainly maintain information from the vaccine in your immune system, you aren't ramping up the actual mechanisms of your immune system like you do when you actually experience influenza.
Think of the temperature raise, the white blood cell production, possible gastro-intestinal reactions - these are all bodily systems being ramped up to a level of performance they don't typically see.
My thought is that if I "successfully" avoid the flu for, say, the next 40 years, those bodily systems will not be as robust - even if I maintain the informational content of the vaccine itself.
Please, please, do not confuse this or lump this in with kooky anti-science, vaccine opponents. I'm just thinking out loud about how stressors on body systems work - which is what my parent was discussing.
If it weren't for vaccinations, and the associated herd immunity, many more people would be dying to it.
I have proposed that the common flu that we all get every 12-18 months serves the same purpose and that attempts to avoid this (via the influenza vaccine) could have unintended consequences for the long term health of our immune system ... but I have never been met with anything but incredulity ...