‘Dearth’ is not a word I commonly use in speech. If I use it, it’s written.
In high school (mumble years ago) a teacher said it’s pronounced so as to rhyme with ‘hearth’; but I cannot find any evidence for that. Every site I check says it rhymes with ‘earth’. So ‘durth’ it is. Where could my teacher have gotten the idea that it is pronounced ‘harth’?
Star Wars? 
Star Wars? 
I have only heard it pronounced to rhyme with “earth.”
I’ve always heard the “rhymes with earth” version, but I also know how it feels to learn that something you were taught by a respected teacher turns out to be incorrect, or at least substandard. That’s a real shock. Makes you wonder if the earth is really flat after all.
And when it turns out that the bad teacher was your parent, your world collapses.
So someone who maintains stockpiles so as to have supplies in time of shortage might be considered a dearth evader?
Good, good. We’ve had a dearth of insidious puns lately.
I pronounce it as God intended, as in the Bible:
“The meek shall inherit dearth.”
Yeah, the pronunciation isn’t in question.
The question is where my teacher might have picked up his or her pronunciation of it.
Actually, the better question may be “where did we pick up our weird pronunciation of ‘hearth’?” AFAICT, it used to rhyme with “earth.”
I learned it as “darth”, too, from a friend from L.A. and Spokane.
My high school was in L.A. County.
WIN
It’s connected to the word “dear”, obviously; dearth is the condition which prevails when things are dear. Could it be that some people’s pronunciation is influenced by that? Admittedly, that would suggest a “deerth” rather than “darth” pronunciation.