Matching parts of the line separately has several advantages. No matching is duplicated. Individual regexes are shorter and extract fewer parameters. Uninteresting lines are discarded sooner. All variables are properly scoped.

use strict;
use warnings;


my $time_stamp = qr{^(\w+) (\d+) (\d{2}:\d{2}:\d{2})};

while (<DATA>) {
    next if !(my($mon, $day, $time) = /$time_stamp/);
    next if !(my($interface, $updown) = $' =~ /.*:\seth(\d): link (up|
+down)/);
    
    if ( $updown eq 'down' ) {
        #... # Process down
        print $time, "\n";
    } 
    else {
        my( $rate, $duplex, $lpa ) = $' =~ /,(\d+)Mbps, ([^,]+), lpa (
+\w+)/;
        next if !defined($lpa); # Invalid 'up' probably never happens.
        #... # Process up
        print $lpa, "\n";
    }
}

__DATA__
May 03 10:15:21 some text: eth3: link down
May 04 10:16:23 some text: eth3: link up,562Mbps, foos, lpa fum
no time
[download]

UPDATE: Refer to @LAST_MATCH_START and @LAST_MATCH_END for documentation on $'.