How about something like this? 
while(<DATA>){
  $before=$count;
  while($_=~/<\/p>/g){$count++}
  if($count>=3){
    @segments=split/<\/p>/;
    for($before..2){
      $toAdd.="$segments[$i]</p>";
      $i++;
    }
    push@keep,$toAdd;
    last;
  }else{
    push@keep,$_;
  }
}
print @keep;
__DATA__
some</p>stuff</p>
</p>other</p>things

[download]
This will let you get around the nasty circumstance of multiple matches per line.
Jason

In reply to Re: Extracting up to a certain string by insensate
in thread Extracting up to a certain string by Jaspersan

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