Note that I said "to first order" (look it up if you don't under what that means) - obviously at some point the diminishing returns sets in and incremental productivity goes to zero. For many enterprises, a good rule of thumb is increased manpower is increased output. Otherwise nobody would hire anyone and they'd just build robots to do everything.
Higher order increases in productivity do come from technological advances. But technology investment is high risk and capital intensive and productivity gains (over the short term, at least) are often smaller than simply increasing manpower. I wasn't ignoring this but for the short term, losses in manpower are typically loses in productivity.
instead of "incremental productivity goes to zero" should be "incremental returns go to zero". Production can go on until a business runs out of resources (money, credit, land, etc). That doesn't mean it can profitably sell the amount of goods produced though.