Like others have said, if you are willing to “play chicken” with them and give your 30 day notice with an offer to lease at the lower rate, I think your chances are pretty good.
However it does sound like you may be negotiating with someone who thinks in terms of “principles” and who doesn’t really understand basic supply/demand and perhaps otherwise lacks common sense. So the “the rent never goes down” rule may prevail in their logic, even though market forces say otherwise. It is difficult to negotiate with someone who doesn’t understand their own best interest.
If you do go for it, don’t flinch before the landlord does!