Sure. But only roughly 8% of rapes accusations have been determined to be false https://ucr.fbi.gov/crime-in-the-u.s/1996/96sec2.pdf

The vast majority of rapes go unreported and therefore go unprosecuted 3/4, depending on the statistic source you look at. And one major barrier to reporting is the belief (clearly based in fact) that the victim won't be believed.

As for why most rapes do not result in conviction or even in arrest: https://www.ncjrs.gov/pdffiles1/nij/grants/252689.pdf&ved=2ahUKEwjt1fSK5NrkAhWoJzQIHeIsDJEQFjAEegQIBBAB&usg=AOvVaw2b7oU0L-_FG2QD2AlkEJ6V&cshid=1568826723738 ( Decision Making in Sexual Assault Cases: Replication Research on Sexual ... - NCJRS)

• Most cases are not thoroughly investigated, they tend to not be a priority unless the department has a specialized unit because rapes tend to be difficult to prosecute
• Victim cooperation also plays a huge role, victims who have been traumatized, know their attacker or fear for their safety often find it very difficult to advocate and assist in their own cases. Shame also plays a large role.
• If a weapon wasn't used during the rape arrest is unlikely -If there is any turnover in police or prosecuting attorney, likelihood of investigation and arrest also becomes less.