We just got off a call with John (thanks John!). I can confirm the following workaround resolved his issue:

Update C:\BasWin20\32bit\protax20.exe.config or C:\ProWin20\32bit\protax20.exe.config with the line in bold, then restart ProSeries:

<appSettings>
<add key="Intuit.TPS.Information" value="TpsBridge-5.13.1" />
<add key="log4net.Config" value="log4net.config" />
<add key="log4net.Config.Watch" value="True" />
<add key="Intuit.Spc.Authorization.EmbeddedWebBrowserImplementation" value="Standard"/>

<appSettings>

This appears to be a problem with a component from another company we use. The line above uses a different component.  We will research the issue and work with the other company to figure out what's going on and resolve it once and for all.