How can I translate "oath-breaker" properly into Latin in reference to losing one's faith?
An oath-breaker is periurus, but note that this word can also refer to a perjurer (one who lies under oath), or a liar, an untruthful person in general.
Although Cicero thought that lying under oath was not periurare (Off. 3, 108):
Non enim falsum iurare periurare est, sed quod ex animi tui sententia iuraris, sicut verbis concipitur more nostro, id non facere periurium est.
⋯ which would be oath-breaking in the strict sense.
A less ambiguous form would be qui, quod iuravit, non facit, or: qui iusiurandum violat.
None of this has anything to do with “losing one's faith,” though.