Here's my go using a flag.

#!/usr/bin/perl

use warnings;
use strict;

my $del_qual;
while (<DATA>){
  if (/^\S/){
    if (/^\w+clk\[\d+\]/){
      $del_qual = 0;
    }
    else{
      $del_qual = 1;
    }
  }
  next if $del_qual and /\s+QUALIFIED/;
  print qq{$_};
}

__DATA__
qclk[6] INPUT (
     ! "asdk fd  sasd"
     VALID ( 
       late_lead 3 ar qclk slope 20
       late_lead 3 af qclk slope 04
       early_dn 8 ar qclk slope 6
       early_up 6 af qclk slope 6
     )
     cext %0.00394757
     cmax %0.005504
     QUALIFIED
)
clkout_qclk_61[3] OUTPUT (
)
clkout_qclk_61[2] OUTPUT (
     REQUIRED ( 
       earlyp  0.5 br qclk clm(2)
       latel_up  5 bf qclk clk(2)
     )
     REQUIRED ( 
       early_lead_dn  0.004 bf qclk clkdom(2)
       late_trail_dn  0.005 br qclk clkdom(2)
     )
     cext %0.0647336
     max_ceff_up %0.187
     QUALIFIED
)
[download]

qclk[6] INPUT (
     ! "asdk fd  sasd"
     VALID ( 
       late_lead 3 ar qclk slope 20
       late_lead 3 af qclk slope 04
       early_dn 8 ar qclk slope 6
       early_up 6 af qclk slope 6
     )
     cext %0.00394757
     cmax %0.005504
     QUALIFIED
)
clkout_qclk_61[3] OUTPUT (
)
clkout_qclk_61[2] OUTPUT (
     REQUIRED ( 
       earlyp  0.5 br qclk clm(2)
       latel_up  5 bf qclk clk(2)
     )
     REQUIRED ( 
       early_lead_dn  0.004 bf qclk clkdom(2)
       late_trail_dn  0.005 br qclk clkdom(2)
     )
     cext %0.0647336
     max_ceff_up %0.187
)
[download]

I've assumed that the start of each record is a non space character in the first column.