Because without error correction the mutation rate goes way up which might get you to squeak by an already alerted immune system and achieve reinfection. That's why you get new strains of the flu all the time. Error correction means that the genome will be very close to the one observed the previous time, so if you want to re-infect you need the immunity to last relatively short or be less than perfect. That secondary (or even later) infection would normally go unnoticed though.