Instead of cron we often use a sub-shell type mechanism. It doesn't do quite what you want but it sort of does.

#!/bin/sh
(while true
do
<script>
sleep 60
done ) &
[download]

This shell will spawn a second shell in memory that will execute your script and once ended (for any reason) restart it in 60 secs. So it's not running on the minute but we find it often does the job.