Maybe you could do a pseudo slurp:

my $slrp = '';
while(<$fh>){
if (/
  ^('domain.com' address bit)$ ## regex to catch lines that match the 
+section start (capturing it too)
/x){
    ## you have found a new section so process the previous one 
    ## provided you have already seen one...
    &process_slrp() if (defined$slrp);
    ## restart the slurp, starting with the new domain.com bit
    ...store $slrp somewhere appropriate...
    ## reset
    $slrp = $1;
    ## start again
  } else {
    ## it isn't the start of a section so stick it into the slurp
    $slrp .= $_;
  }
}
[download]

Although i don't see why you can't slurp the whole file and do a multiline regex?

 m{
    (domain bit.+) ##domain bit and everything until
    Successful downloads:(.*) ## next title, capture everything else u
+ntil..
    Failed downloads:(.*) ## next title, capture everything until...
    etc...
  }mxog
[download]

This way you can directly parse out all the sections, even if they are not defined and stick them in an array to work with afterwards?