Maybe I'm just not paying enough attention, but it looks like you're only trying to append when the file doesn't exist; otherwise you're just looping.

LINE: for ($i=0; defined($i); $i++){ # Loop eternally
  unless (-e "./data/$month.dat") { # If file does not exist, do
    open (FILE, "+>>./data/$month.dat");
    . . .
    close FILE;
    last LINE; # Loop will only exit if file did not exist
  }
}
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Impossible Robot