I'd say about 75% of our guests bring pets.

You can shop insurers that allow restricted breeds (often at higher premiums), require renters insurance with pet liability naming you as additionally insured, or adjust your pet policy to clearly exclude prohibited breeds so expectations are set upfront. 

If the tenant destroys the place but the pet didn’t you can only keep the non pet SD portion. 

One way is to say pets considered or set a number.

Since a 10 day notice includes the option of the tenant to "cure" the problem, is there anything I have do do differently do avoid doing it over and over?

Please make sure you know all of this including required notice periods before you violate any fair housing laws or lose any lawsuits.

In addition to requiring better pet hygiene, removing the carpet in the upper unit and replacing it with vinyl plank flooring would help since it is a lot easier to clean and won't retain the odor as readily however the carpet likely helps to dampen some of the sound from the upper unit.  

If you really don't want more than one make the pet deposit high so it will be worth your while for those willing to pay. 

Jose, do you include your appliant criteria in you listing (step 1?)

No pets is also probably hurting you.Otherwise, lower price 5% every 3-4 weeks until activity picks up.FYI - Nov-Feb is worst time of year for real estate due to Holiday Effect.