We apologize for the delay in getting back to you on this post. We appreciate your post.
A proxy IP address shouldn't changed based on what user is signed in. In most cases, a proxy server would utilize a static IP to ensure that the proxy is consistent across all users.
As for the downloading issues, this could be due to the local system account not being able to get through the proxy. All scheduled downloads of the patches would be utilizing the local system account. If your proxy is configured for user based authentication versus machine or anonymous authentication, this could happen as the system account doesn't have a way to supply any credentials to the proxy to verify it has permissions to download the files.