I'm guessing that it's because you're mixing /x in $re_line with the plain regexp in $re_ip. This worked fine for me:

#!/usr/bin/perl

while( <DATA> ){
    chomp;
    my $re_ip   = qr/(\d+\.\d+\.\d+\.\d+):\d+/x;   # added /x here    
+                  
    my $re_line = qr/ ^ \s* $re_ip \s* -> \s* $re_ip \s* -> \s* $re_ip
+ /x;
    my @results = /$re_line/; 
    printf "%-18s %-18s %-18s\n", @results;        
}
 
__DATA__
136.1.1.154:33672 ->  64.210.209.51:80 ->  192.168.1.145:80        tcp
65.201.211.176:14664 ->  64.210.209.54:80 ->   192.168.1.78:80        
+   tcp
   67.38.95.86:2116 ->  64.210.209.50:80 ->  192.168.1.103:80         
+ tcp 
198.49.222.246:52469 ->  64.210.209.54:80 ->   192.168.1.79:80        
+  tcp
193.80.106.152:3781 ->  64.210.209.61:80 ->   192.168.1.81:80         
+ tcp 
   67.28.79.24:3248 ->  64.210.209.54:80 ->   192.168.1.79:80         
+tcp
128.187.192.39:1218 ->  64.210.209.54:80 ->   192.168.1.78:80         
+tcp
128.187.192.39:1209 ->  64.210.209.51:80 ->  192.168.1.144:80         
+tcp
[download]

--
Love justice; desire mercy.