Are you maybe leaving behind stuff in the environment upon every iteration?  On most Unixes, the command line arguments share a fixed space with the process' environment.

For example, the following would reproduce the issue (tested on Linux):

#!/usr/bin/perl

for (1..10) {
    $ENV{JUNK} .= "ABC" x 5000;
    
    my $begin_load = `cat /proc/loadavg`;
    warn "cat failed: $!" if $?;

    print $begin_load;
}
__END__
0.56 0.43 0.25 1/219 27522
0.56 0.43 0.25 3/219 27523
0.56 0.43 0.25 2/219 27524
0.56 0.43 0.25 2/219 27525
0.56 0.43 0.25 2/219 27526
0.56 0.43 0.25 2/219 27527
0.56 0.43 0.25 3/219 27528
0.56 0.43 0.25 3/219 27529
cat failed: Argument list too long at ./757540.pl line 7.
cat failed: Argument list too long at ./757540.pl line 7.
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