I fixed the problem by multiplying the number of input files by 60 and using this as my timeout value... The script below now works:

use strict;
use Net::Telnet;
use Net::FTP;
use Time::Local;

my $name = 'USER';
my $passwd = 'PASSWORD';
my $host = 'HOST';
my $prompt = '/MACHINENAME\$/';

my($sdate,$edate,$outfile) = @ARGV;

$outfile = uc($outfile); #VMS puts files in uppercase

my $command = 'some command';

# Assume each file in a specified date range will take 60
# seconds to process. Multiply
# this by 60 to get the timeout value. Large, but we don't
# have to deal with timeout problems

#Work out how many days in specified range:
my($sday,$smon,$syear) = split('-',$sdate);
my($eday,$emon,$eyear) = split('-',$edate);
my $time1 = timelocal(0,0,0,$sday,$smon,$syear);
my $time2 = timelocal(59,59,23,$eday,$emon,$eyear);
my $difference = $time2 - $time1;
my $days = sprintf("%3.0f", $difference / (60*60*24) );
my $timeout = $days * 60;

my $telnet = Net::Telnet->new(
                  Prompt     => "/$prompt/",
                  Input_Log  => 'input.log',
                  Output_Log => 'output.log',
                  Host       => $host,
                  Timeout    => $timeout
                 );

$telnet->login(Name => $name,
           Password => $passwd,
           Prompt  => "/$prompt/",
          );

$telnet->cmd($command);

$telnet->print("lo");
$telnet->close;

my $ftp = Net::FTP->new("$host", Debug => 1);
$ftp->login($name,$passwd);
$ftp->get("$outfile.CSV");
$ftp->delete("$outfile.CSV");
$ftp->quit;

exit;
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