Why aren't Dwarves immortal?

Ever since I read the Silmarillion, I've been wondering why the Dwarves were created mortal. Since mortality is the gift of men from Ilúvatar, it didn't make sense to me that Dwarves also have the same gift. Moreover, everyone at that time was immortal, so what made Aulë decide that the Dwarves should be different in that aspect?

I've read The Lord of The Rings and the Silmarillion, but none of the other works of Tolkien. Did I miss something, or is the reason explained in the other resources?

From the Silmarillon, on the creation of the Dwarves (copied from the wiki page):

Since they were to come in the days of the power of Melkor, Aulë made the dwarves strong to endure. Therefore they are stone-hard, stubborn, fast in friendship and in enmity, and they suffer toil and hunger and hurt of body more hardily than all other speaking peoples; and they live long, far beyond the span of Men, yet not forever.

^{(emphasis mine)}