Ask them if you're using a shared IP address. If you are, then ask if you can get a unique, static IP address (or a dynamic address). Both will help you out.
You said you have T3, but I think most likely it's something else. In the US, nothing higher than T1 can be placed in a residential zone. And, a T1 is very expensive to have. From what you're having trouble with, it sounds more like you have cable. Cable often uses the same IP for the entire neighborhood. And if more than the minimum number of connections from the same IP is reached (this can range from 2 or 3 up to a lot), you'll get that error. When people start logging off, then you are able to log on.
