I'm influenced by Lisp's With-Open-File forms in wanting this code to look more like:

open my $log, '>>', $logfile and do {
  # lots of stuff to log
  1;
} || do {
  print "Failed to write log file $logfile: $!\n";
  die "Failed to write log file $logfile: $!\n";
}
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This has the interesting attribute that if the first do-block does not return true, the error handling block runs for it, possibly allowing multiple error types to be more-or-less gracefully handled together. For many things that's a benefit (but certainly not always)