As far as I know, set_time_limit() is designed to pretty much kill the script, and really just lets you reset the time_limit option from the php.ini file. I don't know if you can continue running the script after that execution is hit, it's rather like a hard limit.
What you could do rather than use set_time_limit() is a while() loop that checks a time variable and when it hits 60 seconds, break out and display a message.