Here is the underwriting rule referencing your situation (direct from Fannie Mae guidelines):
"Requirements for Existing Construction - When There are Incomplete Items or Conditions that Do Affect the Safety, Soundness, or Structural Integrity of the Property
When there are incomplete items or conditions that do affect the safety, soundness, or structural integrity of the property, the property must be appraised subject to completion of the specific alterations or repairs. These items can include a partially completed addition or renovation, or physical deficiencies that could affect the safety, soundness, or structural integrity of the improvements, including but not limited to, cracks or settlement in the foundation, water seepage, active roof leaks, curled or cupped roof shingles, or inadequate electrical service or
plumbing fixtures. In such cases, the lender must obtain a certificate of completion from the
appraiser before the mortgage is delivered to Fannie Mae. Although the original appraiser should
complete any required certification of completion, the lender may use a substitute appraiser."
Since this is a somewhat major renovation (as opposed to something minor like remodelling a bathroom), you're going to have to wait to complete the refinance. It's not a value issue - it's just not eligible right now.
This is not something that would normally come up in taking an application, so I think you probably should have asked the lender up front if this would be a problem. The application fee most likely went to pay for the appraisal and in most cases you receive a disclosure at the time of application stating under what conditions, if any, an application fee is refundable.
If you paid to apply for the loan AND for the appraisal, then I would politely ask if the lender would be willing to carry the application fee forward when the renovations are complete and you are ready to re-apply. There are some companies (I can think of one - it rhymes with "Chicken Loans") that tell you sorry, once you apply this fee is non-refundable no exceptions. I will normally work with the borrower to find an good compromise and apply things towards their future transaction. If they are not willing to work with you then finish your renovations and take your business elsewhere.
Hope this helps!