I think this is normal sunflower behavior.
Here is my reasoning. We started growing sunflowers because we were "vandalized". Three years ago my neighbor, and sometimes partner in gardening adventures, snuck into my yard and creatively vandalized a couple of empty spots by planting a dozen or so sunflowers that had come up as volunteers in his yard. I didn't pay any attention to them until they started to flower, and then I noticed that the lower leaves were dying and falling off, even as the tops of the plants were growing ever upward and putting on more new leaves.
I have just assumed this was normal sunflower behavior. We grow a few for the seeds and they are in a row by themselves. I snip off the ugly leaves, but purely for aesthetic reasons.
The rest of the sunflowers grow in the jumble of flowers in the kids gardens. In among the cosmos, batchelors buttons, sweet alyssum, mixed poppies, sweet william, columbine, etc, the lower stems of the sunflowers are hidden by the other plants so I don't really notice the dead leaves.
My new answering machine message:
Hello and thank you for calling. We have been members of the NRA since we were old enough to take communion. As a Christian family, we have no interest in your robotic messages of hatred, bigotry and fear. We choose to vote for love, hope, and change, and we hope you will join us. Have a great day!.