Two defective pieces in a row - unreasonable to demand refund?

How long have you had the replacement unit?

The most likely problem is an improperly seated connector inside the unit. It’s very likely that your dealer can locate this and correct it for you. Of course that doesn’t really answer your question.

Do you have a relationship with this dealer? You might want to consider that as part of deciding what to do next.

But to answer your question: Yes, strictly speaking, I think you’re entitled to a refund. So far, you haven’t received what you paid for. That the dealer has a "no refund" policy doesn’t matter. He hasn’t delivered.

I'd give the dealer a chance to examine what might be wrong with the second unit. But I'd also be inclined to consider a third unit that - as @dweller sez - is checked first at the store.