can a cat go deaf from ear mites?

  So I took In this stray cat and took her to the vet, they gave her shots and did blood work and every thing was fine but she had a wicked bad ear mite infection.Now the ear mites are all gone and she is like a brand new kitty but I wonder if it has affected her hearing. I could take her in to the vet again

but I already spent over $ 850 on her vet bills and special food. Does it matter if she is deaf if she stays inside?
Hearing is essential for knowing when danger is coming (think a large dog running at her, or a car ). If you think your cat is deaf, don't let her outside until you know for sure. Sneak up behind your cat when they are sleeping, or better yet when she is half dozed, and clap your hands. If your cat's ears don't turn back towards the noise then it is likely she has some hearing loss. A bad case of ear mites can cause hearing loss if the ear canal gets infected. It could be that the ears are just infected right now and the pus and fluid in the inner ear is effecting her hearing temporarily. Call the vet and see if she'll call in antibiotics for you without a vet exam (since you've been there recently). Sometimes my vet will do that if the cat was there very recently.
Ear mites can damage the ear canal. Clap around her at different lengths and see if you have a reaction. Keep her inside because she would be defenseless outside not being able to hear danger approaching.
It may have. Hard to tell. Do her ears move at all?

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She'll be fine indoors.