Quick fix, you can work to beautify it:

#!/usr/bin/perl

my $MaxLineLength = 8060;
$search = '<COLUMNS>';
$replace = '<DATA>';
$searchEnd = '</COLUMNS>';
$replaceEnd = '</DATA>';
$fileContents = '';

my $linePrefix = '';

while (<STDIN>) {
   chomp; # Remove newline
   if (/(^<DATA>\t).*(<\/DATA>$)/) {
      if (length() <= $MaxLineLength) {
         print $linePrefix; # Empty only for first line
         print;
         $linePrefix = "\n";
      }
   }
   elsif (/(^<COLUMNS>\t).*(<\/COLUMNS>$)/) {
      s/$search/$replace/g;
      s/$searchEnd/$replaceEnd/g;
      print $linePrefix;
      print;
      $linePrefix = "\n";
   }
}
[download]

Basically, you remove newlines from what you read in, then output newlines before printing a line, not after. The only exception is the first line, of course.

As you may imagine, I'm too lazy to test it - basically because I don't want to write an example file :)

OFF-TOPIC Update: note that your node had been considered in order to remove the ------------------------------------------------ line at the beginning of the script. This is due to the fact that in Unix-like environments having #!/usr/bin/perl at the very beginning (I mean, starting from the first character) allows automatic selection of the interpreter. You can edit and remove them by yourself :)