Unless you are running BGP and are receiving full Internet routing table, you are very unlikely to run into this issue. Routers are vulnerable only for TCP sessions terminating on the router itself not session going through it.
You should do a "sh proc cpu" when the CPU on the router hits 99% to see which process is chewing up the CPU cycles.
Hope this help,
Regards,
Harold Ritter, CCIE #4168 (EI, SP)