Four-year-old Missey disappeared from outside Austen Mewes' home on Leasowe Avenue in Hunslet on October 11.
It is thought the dog has been stolen for breeding - but she has a condition called Brucellosis which means any puppies she gives birth to will die and possibly kill her too.
Alison Bell, a volunteer and co-founder of Animal Aid, is now searching for Missey.
Mrs Bell said: "She's a beautiful dog, she's got bright blue eyes and [would seem] perfect for breeding.
"But the puppies will certainly die and there's a 90 per cent chance it will kill Missey.
"Austen's just devastated, he's at the end of his tether. We know somebody's got her."
Mrs Bell said she would beg anybody who has Missey to return her.
She said: "If their plans are to breed her, she's of no use. They're not going to make money."
Animal Aid helps to reunite dog owners with their missing pets.
Anyone who has information about Missey can contact Mrs Bell by emailing [email protected]