Speak with your agent about this.....
Good luck and best,
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Sellers who refuse to do this are generally refusing to face reality, and their Realtor should be asking them,"Why do you believe that the next buyer will get an appraisal that's any different from this one and if you do believe it's will be different, what makes you think it will be higher and not lower? If you want to sell this is the price you're going to have to live with."
Alternately if you honestly believe the appraiser made some mistakes in their valuation you, your Realtor and/or lender could request them to review their work and I would suggest your Realtor supply them with comps they may not have considered.
Finally you could simply choose to pay the difference though I'm not certain why you would want to do this unless you really felt the property was worth more than the appraiser felt it was.
Regardless of what happens the money you spent on the appraiser and on inspections is gone.
As for whether you can get any money back, it depends on whether you have that clause specified in your contract.