I'm not sure why you are seeing this only in LV 7.1.1. My first question is whether you have already downloaded the f2 patch for 7.1.1, which adds support for .NET 2.0. I know that you aren't wanting to use .NET 2.0, but I would suggest you make sure that is installed.
Second, since it works in 8.0, I figure this is already true, but just in case - is your config file with the requiredRuntime named LabVIEW.exe.config and is it in the same directory as LabVIEW?
Third, again you should have done this for 8.0, but make sure you have installed the SP1 service pack for .NET 1.1 (download from Microsoft).