Is there a limit by sending DHCP Requests and Reponds too many times? Or Ping? No :-)
The cache will never get overloaded, however if you flood a computer with Arp packets
it might crash due to a DoS condition. I'm not sure if this is true though but try it out.
Just keep in mind, that when you stop arp spoofing one problem might occur:
All clients that were arp spoofed might loose connection to A) The whole network
or B) The internet due to you might be aggregating gateway and then the other
computers on the network will think they have to go through you.
Of course the cache will eventually clear itself.