A giyoret who made one small mistake - Igrot Moshe Yoreh Deah 3:108

In 1979, Rav Moshe Feinstein was approached by a גיורת was was concerned that her conversion was invalid. As she was going to the mikveh, she excitedly told a friend of hers what she was doing. Her friend asked her how she was going to manage to tell her bosses that she would be missing work for Yom Tov. With Pesach on the horizon, the woman had thoughts to slip into work on the last days of Yom Tov so as to avoid any confrontation that might cost her her job. In fact, she did go to work those days, but only carried the necessary subway tokens, and did not do any writing while at work. Since that one time, which occurred soon after her conversion, she had been living a fully observant and dedicated lifestyle. Her fear was that since she was thinking about going into work on Yom Tov while she was in the mikveh, perhaps that counted as not accepting even one mitzva, and would thus invalidate her conversion.

Rav Moshe ruled that her conversion was completely fine, on multiple grounds:

1. She is not believed insofar as believing her would make her forbidden to her husband and cast aspersions on her children.
2. Her alleged thought counts as דברים שבלב, which cannot outweigh her explicit statement to the בית דין administering her tevila that she was accepting all of the mitzvot.
3. If a convert were to say that he was accepting all of the mitzvot but he did not think he could withstand a יהרג ואל יעבר situation, his conversion would be good anyway. Rav Moshe brings three proofs for this point (including the fact that someone who converts for marriage purposes is considered to be a valid convert, even though such a person is certainly not thinking of giving up his life for mitzvot), and concludes that the fear of losing one's job is a similar pressure that many people have a hard time withstanding, and thus it should not invalidate the conversion.
4. This woman had been living a strictly observant life for the past ten years, a fact that was known to all, and thus her initial transgression was clearly not indicative of a lack of a desire to keep any mitzva.