I'm working as a root so I should have permission to create any file

That is simply not true. There are a number of possibilities that can prevent even root to write to a file (or create it):

• file is readonly
• directory if readonly
• filesystem is readonly (for example CDROM)
• out of filehandles
• out of memory
• disk full
• file system errors that implicitly make the filesystem readonly
• file locked by another program
• directory locked by another program (most likely kernel during some directory move operations)
• file on a network filesystem where you don't have permissions
• Some "virtual" files can't be written to (/proc/*)
• ...The list goes on and on and on to ever more obscure "error" conditions...

BREW /very/strong/coffee HTTP/1.1
Host: goodmorning.example.com

418 I'm a teapot

This is working on my pc.

use strict;
use warnings;

my($NEXT_TIME,$FILE_NUMBER,$LOG_FILE);

$NEXT_TIME=time;
$FILE_NUMBER=0;

while(1){
    if ( time > $NEXT_TIME )
    {
          print "Change file next=$NEXT_TIME\n";
          thread_log();
    }
}

sub thread_log
{
#closing the handler to the current file
if ( -e "log$FILE_NUMBER.log" )
{
  close($LOG_FILE);
}

$FILE_NUMBER += 1;
open( $LOG_FILE, '>', "log$FILE_NUMBER.log" ) 
    or die "Unable to open logfile:$!\n";

$NEXT_TIME = $NEXT_TIME + 10;
}
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It seems the problem is in other place. How you invoke threads?