I think three things contributed to its downfall:
1) Perl 6
2) the huge inflow of people into Unix who were not keen on Perl's ultra-Unixy wackiness (let's borrow from bash, awk, regexps and everything under the sun! - fun but not exactly welcoming to require newcomers to learn the entire cultural history of Unix to learn your language)
3) the fact that sysadmin work was quickly graduating from writing scripts that send angry emails when users fill their 20MB home directory quota into managing serious, distributed system that serve as crucial infrastructure, for which the non-wackiness of Python was a better cultural fit (particularly when the role of developer and sysadmin started to merge)
It's not so much that people started rewriting their Perl scripts, it's more like the newcomers who weren't doing Perl soon outnumbered those who were.