The oldest software still used is operated by banks, government agencies, schools and businesses. A large number of them are black boxes, and very expensive, so nobody will replace them. Their hardware just gets maintained ad infinitum, and the software doesn't care how old it is, so it just keeps running.

So basically, the age of software is limited by its hardware. (It's similar with animals: if nobody bumps them off and the hardware keeps ticking, the software probably will too... fish and mammals can live for hundreds of years)