I interpret what JK Rowling has said to mean that however many Dementors already exist cannot be destroyed by any means, Wizarding or human, meaning there is no spell, potion, curse, etc, that will eradicate them. I expect there is the possibility that Dementors eventually die a natural death. I suspect that the number of Dementors in the world ebbs and flows with their contact with a ready supply of despair, unhappiness, degradation, hopelessness, etc. The less of these emotions they have to feed off of, the less Dementors there will be.
I think it's analagous, as JKR herself says, to depression. Depression is a condition that is never cured, but its severity can possibly be controlled with therapy, medications, and by tweaking other external factors that make it less likely for the depression to be debilitating, if that makes sense.
Anyhow, this is my interpretation of what JKR has said about Dementors.