SANAA, Jan 31 (Reuters) - Yemen rejected a ceasefire offer from Shi'ite rebels on Sunday and said fighting was continuing, as neighbouring Saudi Arabia accused the insurgents of mounting sniper attacks inside its territory. The conflict with the northern rebels, who complain of social, religious and economic discrimination in the southern Arabian state, has rumbled on since 2004, but intensified last year and drew in oil-rich Saudi Arabia. Yemen is also struggling against al Qaeda and southern secessionists, and Western powers fear it could become a failed state. The U.S. State Department's counterterrorism chief was visiting Yemen on Sunday, state...