Cycling = looping.
Most servers have a php script maximum execution time of either 30 or 60 seconds. Now if you have a 60 second max then you could easily loop a script for 59 seconds (with a sleep between each loop to stop your host shutting you down for CPU hogging). That means that every time the script loops it will check for any files in directory A and copy them into directory B with a new name.
On the 60th second your cron triggers a new version of the script to run and the whole process starts again for another 59 seconds.
If you're unsure of how to set this up, I can do the initial checks of your environment for you (checking max exec time etc) to see if its suitable but if you want the code written by me it would be chargeable.