It looks like you'll need to parse the log file into log events first, before dealing with the XML content; e.g. something like:

my @logentries = ();
my $toss = 1;
my $monthRegex = join("|",qw/Jan Feb Mar Apr May Jun Jul Aug Sep Oct N
+ov Dec/);
while (<LOGDATA>) {
   if(/^($monthRegex)\s+d{1,2}\s+(\d{2}:){3}/) {
      push(@logentries,$_); $toss = 0;
      # unless you want to ignore some of'em
      # in which case: $toss++;
   } else {
      $logentries[$#logentries] .= $_ unless $toss;
   }
}
foreach (@logentries) {
# decide what to do with each entry,
# handling XML content with a suitable module when necessary
}
[download]

No doubt someone knows of a module for recognizing dates in log files, but I think it's a simple-enough issue that coding this part from scratch is just as easy.

If the log is really big and you don't want an array eating up that much memory, this alternative while loop would work:

my $entry = "";
while (<LOGDATA>) {
   if(/^($monthRegex)\s+d{1,2}\s+(\d{2}:){3}/) {
      $result = &handleEntry( $entry ) if $entry;
      $entry = $_; # unless you want to ignore some of'em
      # in which case: $entry = "";
   } else {
      $entry .= $_ if $entry;
   }
}
$result = &handleEntry( $entry ) if $entry;
# and replace the "foreach" loop in the previous version
# with "sub handleEntry { ... }"
[download]

update: fixed some commentary about setting $entry = "" inside the while loop
update: added the $toss and fixed commentary in the first example, and fixed the second example (again!) so that extra lines from a "tossed" entry get ignored properly.