Is it easier to get pregnant with mirena when the strings disappear?
I had a mirena put in in 2006, and the strings periodically went missing, but the mirena was still in place. I didn't get pregnant. If the strings are missing because the mirena fell out then you are as likely as the next unprotected woman to be pregnant. If the strings are gone but the mirena is not then it depends on many factors such as the actual location of the mirena and the shape of your uterus.
Did you do an HPT?