Do Catholics have to go to Marian shrines like Fatima once a year?

There’s zero obligation for Catholics to go to Marian shrines. The decision to visit them is totally voluntary. Many shrines do attract large numbers of pilgrims; the Marian apparition site at Lourdes, France, for example, attracts about five million pilgrims a year. Some come in hope for healing (the spring at Lourdes has been associated with miraculous physical cures), while others come hoping to enrich their prayer lives, while others come out of curiosity. But Catholics are not required to visit any shrine, Marian or otherwise, during their lives.