Uh in the book Durin's Day isn't a yearly thing and that really was the only chance. I blame PJ for his poor choices since he went against so much Tolkien canon but please read the books and pay attention because this is the second time your tag meta that's more headcanon than canon has been posted around like it's canon fact.
this is what the book says about Durin’s Day:
"Then what is Durin’s Day?" asked Elrond.
"The first day of the dwarves’ New Year," said Thorin, "is as all should know the first, day of the last moon of Autumn on the threshold of Winter. We still call it Durin’s Day when the last moon of Autumn and the sun are in the sky together. But this will not help us much, I fear, for it passes our skill in these days to guess when such a time will come again."
so yes, Durin’s Day isn’t EVERY first day of the last moon of Autumn, but only those when the moon and the sun happen to appear in the sky together. now, Thorin basically says ‘we are not astronomers and we have no fucking clue when this is going to occur again’. I am no astronomer either, and I lack the time to do my research right now. Tolkien Gateway calls it a rare occurrence, while the LoTR Wikia calls it a yearly thing, so you know what, I’m going to ignore you telling me to ‘read the books and pay attention’, and just go with whatever floats my goddamn boat if you don’t mind