Effectively what you want to do is remove any blank lines and then join every second remaining to it's predecessor. So... (untested)

#open INPUT and OUTPUT
while (<INPUT>) {
    chomp;
    next if m/^\s+$/;
    my $nextline;
    chomp($nextline = <INPUT> ) while $nextline !~ m/^\s+/;
    print OUTPUT $_,' ',$nextline;
}
#close INPUT and OUTPUT
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