I noticed this problem a few weeks ago after I tried to login my account after Gold had lapsed. I got the error where it said it could not connect to XBox live. I tested the connection and it was OK. I knew that already because throughout this whole process I can use my son's Gold account on the same machine OK.
I eventually got to the point where it suggested to redownload the profile. I tried that, but it says it cannot download profiles at this time.
I got the bright I idea to use my 2-day code I got with Halo Anniv. That fixed it...for two days.
Now I have the same problem I described above. I am using a "free" live account but I can't login or download my profile. The other Gold live account on the same machine works just fine.