Thanks for your help. I found the solution.
Apparently there are a few different places to set the query and login timeouts. There are two places that I now know of in EM and another in QA. Although I set the timeout to unlimited in EP by right clicking on the server, then properties - then connections - I didn't set it in QA (Tools-Options-Connections). I also didn't set it in EM (Tools-Options-Advanced). Once I set these then I solved my problem. Perhaps in future versions of SqlServer Microsoft will add another 50 ways of setting this property.