Hello, intentional limit on the server - is an usual practice with world-wide picture services.
To avoid it it's need use proxies or proceed sequental downloading from several IP addresses.
As per your project, for example I can write for you simple script that will use all mine 4 vps (each has unical IP) to help you with downloading, or try to assign some proxies list for that purpose.
So your task is more about way to download resource than something about GIS or spatial data. Please provide simple URL to try to get sequenec of pictures to see how that will block after 5 minutes, and how much time that will take to unblock the script. Thanks