Amazon RDS CPU Usage keep increasing without any long running process in Show Processlist
You should keep an eye on things like your buffer sizes, table cache, query cache and innodb_buffer_pool_size, key_buffer_size as all of these memory allocations can have an affect on query performance which can cause MySQL to eat up CPU.
Enable slow query log and see if there are queries getting logged there. 
Observe "mysqladmin status" output for sometime certain values like "Questions, Slow queries, Open tables, Queries per second avg" should help.