Two years ago, the IRS stated we didn’t claim an additional $5000 of income. We provided proof and it was settled. A new agent reviews and the cycle starts over again.

Normally the IRS cannot audit you for the same thing twice so you probably need professional assistance.  Maybe you can get free help from the taxpayer's advocate office.    See this IRS website for Taxpayer Advocate in your area and a toll free number - http://www.irs.gov/Advocate/Local-Taxpayer-Advocate