It looks like you can use Archive::Zip to open up a Zip file.

use Archive::Zip;

my $zip = Archive::Zip->new("yourfile.zip");
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Once you have the Zip file opened, use the members() method to get a list of files contained in the Zip archive, and loop over them:

my @members = $zip->members();

foreach my $member (@members) {
  # ...
}
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Where the # ... is is where the interesting bits of your code need to go. In order to check out the last modified time of the $fh you have, call $member->lastModTime().

So let's put this together...

#!/usr/bin/perl -T

use strict;
use warnings;
use Archive::Zip;

my $zip     = Archive::Zip->new("file.zip");
my $members = $zip->members();

my $firstdate;
my $lastdate;   # No need to fill these in with "never", because I hav
+e had dates before.  ;-)

foreach my $member (@members) {
  my $filedate = $member->lastModTime();

  if (($filedate < $firstdate) || (!defined($firstdate)) {
    $firstdate = $filedate;
  }
  if ((!defined($lastdate) || ($filedate > $lastdate)) {
    $lastdate = $filedate;
  }
}

$fh->close();

# Calculate the difference between the first and last
# file dates...
my $datediff = $lastdate - $firstdate;

# Check if the time difference between the first and last
# files is more than 3 months...
if ($datediff > (60 * 60 * 24 * 30 * 3)) {
  # You need a new file
}
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Please note that this code is completely untested, but it should at least be a reasonable start...