I can't reproduce that:

my $foo = "stuff";
@data = <DATA>;

foreach (@data) {
  s/XXYY/$foo/;
  print;
}
__DATA__
<XXYY>
XXYY XXYY
test
[download]

gives the following output:

>perl -w tmp.pl
<stuff>
stuff XXYY
test
[download]

Maybe you are looking at the wrong output file?

In any case, you most likely want a /g at the end of your substitution, so that the second input line becomes stuff stuff on output.