How many years can extra marital affair go undetected ?

Why? Are you having one? Do you think your partner is having one? Sooner or later, would be my general reply to your very general question.

In almost all cases the wife knows about the affair within weeks at most.  But because of "face" she keeps that knowledge to herself.  It is better to pretend it isn't happening than to destroy everything that you love.  People like to delude themselves that they have "got away with it".

If you have the chance to expose them, do. Some people are expert liars and can carry these things on for years. There is really no time limit.

I knew someone who was married for 20 years and had an affair even longer than that.

They cheaped on their first X with the same person.

Then moved to #3 marriage...& continued to cheat with the same person.

Depends on how dumb the other spouse is. It can be detected after the first time or could go on for much longer. Soon or later they all get caught as they should be. 

Some can't even go a full day

undetected, some go to the 

grave and never known about. 

Why?

I had one that went 17 years.

They could go on forever. I've read stories about women (and men) who find out their spouses were carrying on an affair for decades.