Thanks, I did not realize the dangers of lexicals in this situation. Though in order to get the capture variable behavior of the OP's code, I made the following changes:

...
    $str =~ s/$re(?(?{++$cnt > $times})\A)/qq["$repl"]/gee;
...

limited_re("111111111",qr/(1)/,'${1}5',2);
[download]

Though it would have worked with the code as it was if you included double quotes inside the single quotes of the replacement string, e.g., '"${1}5"'.