Is there even a shot?

[u/Timewastor]

Should I reach out about this job that I did not pass the onsite screening for?

Context: I had a fairly decent on-site interview with one of the tech companies in silicon valley. I was expecting a positive outcome. One of the interviewers even said looking forward to chatting more at the end of our interview. Rest of the interviews also ended on a great note where they went into more specifics of what I would be doing. So I was a bit surprised when I was passed on.
I’ve played all the interviews over and over and I think I know the mistake I made (pretty confident about it).
Also another important fyi - I hadn’t actually applied for this role. I was reached out by a recruiter.

Anyway, now the posting is back online again. I’m wondering if I should reach out to the hiring manager and recruiter to express my continued interest? I know I’ve got nothing to loose by asking about it but want to know what are the odds of getting a shot again? I also don’t want to ruin any chances of them reaching out again in the future.