I have a real life example, not just an estimate.
It actually takes quite a while! There is a kid in my school, and he's been in my school since grade 8 (i'm in grade 11 now) and he has worn the same sweater and jeans since grade 8. It is one plain black sweater, and crappy pair of jeans. It's disgusting, but back to the topic!
Back in grade 8, I didn't really notice. It's not something that occurs to people, unless you like memorize what EVERYBODY in your school wears, and you check every day to make sure it is different.
I found out (Was told) in grade 9 that he wears the same thing every day (He is my friend, I see him and talk every day) and I was just like whoah! Because I did not even notice. So I'd say it takes about 5-8 months for somebody to realize somebody is wearing the same thing over and over again, or if its a close friend, I bet its alot faster, maybe like 3-5 weeks.
*EDIT* After I posted this I realized everybody said about 2 days, so I realized I forgot to add that he is sort of a loser / loner so that might affect the time scale :D