When using splice in a loop like that, don't forget to reverse the indices. (Splicing at index N doesn't affect indices 0..N-1, but it does map indices N+1..$#END to N..$#END-1.) And you should specify the length (1, in this case) of the array to be spliced out.

e.g. Using your code, with @dirs = qw/A B C/;, and running "touch A/analysis_completed" from another shell.

$ tree
.
|-- 503170.pl
|-- A
|-- B
`-- C
$ perl -l 503170.pl
All done
$ tree
.
|-- 503170.pl
|-- A
|   `-- analysis_completed
|-- B
`-- C
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When A/analysis_completed exists, your code splices the entire @rFiles array. The following would do the right thing:

my @dirs = qw[ ... ];
my @rFiles = map{ "$_/analysis_completed" } @dirs;

while (@rFiles and sleep 15) {
    -e $rFiles[$_] and splice @rFiles, $_, 1 for reverse 0..$#rFiles;
}
print "All done";
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