Banks can refuse to cash a paycheck if it has been 6 months or more past the check's issue date, as reported by Forbes. This policy is according to the Uniform Commercial Code, and applies to both business and personal checks. A bank can choose to honor a 6-month old check, but it is up to the bank's discretion to process it or not.
After a period of 3 years, almost all states' policies insist that banks turn over the funds from unredeemed checks to the state, as stated on the Banking Questions website. Most states require that an individual must file a claim with the government to receive unclaimed wages.