Contact the IRS about refund

I e-filed my return back in April, then I got a letter saying I owed more tax. I replied to the letter both in writing and by phone (several times). I have not received a reply to my letter but have been told three times on the phone that the IRS agree with my argument and twice I was given dates in June to get the refund. Neither date was met.

Today. my wife and I have been on the phone for 5 hours and the agent we spoke to confirmed we will get the refund but seemed vague as to when!

My question to the community is: Do you have any advice on how I should proceed eg get a lawyer involved etc? There is a significant amount of money involved.