As a Kentucky native myself, I'm not super hopeful that this story is going away anytime soon. First, since she's an elected official, she can't just be fired/terminated, she has to be impeached. Which means the state House has to indict her on impeachment charges and then Senate has to try her. However, the majority of Kentucky voters at the very least support her religious opposition, with a smaller majority opposing gay marriage altogether, so of course they back her and don't understand that it's really just a matter of her refusing to do her official duties. That makes trying to impeach her difficult politically.
So, if she's not impeached, she will remain in office and continue to deny marriage licenses to any couples. Since her stay was officially denied by the Supreme Court, obligating her to comply with the law but still allowing her to pursue her original appeal, she could be held in contempt of court, which means she risks jail time or hefty fines. Then one of two things happens: 1) She goes to jail and essentially becomes a martyr for the religious right and gains large amounts of sympathy from Kentuckians and other people nationwide; or 2) She's fined and will never have to pay a cent because it will either come out of tax payer money (since she's an elected official) or there will be large crowdfunding campaigns to gain donations for her that will likely surpass her fines and ultimately make her richer than before this all started.
It's unfortunately a pretty pessimistic outlook, but that's just kinda how I see this all playing out. The fight's nowhere near over.