I’ve been rejected 5 times from Google. And yet every year like clockwork they email me again asking to interview. At this point I just say yes every couple of years and try again because why not. I think I do well enough to deserve a call-back but never good enough to get hired (I made it to the hiring committee though).
I "failed" my first four (edit: onsite) FANG interviews. 5th time was a charm, have been happily employed with a senior title at FANG for a couple years.
Not exactly new information to HN, but the job itself is quite a bit easier than the interviews (wrt to technical knowledge). It can be just as stressful though (I actually think stress response / teamwork is one of the main things FANG interviewers are looking for after a certain bar of technical competence is met, YMMV).
This isn't for everyone, but if it's something you really want to do, don't let the rejections get you down. You'll get in eventually :)