I've been having random disconnects from Xbox Live for over a month now. I read today that deleting your profile and re-downloading it can fix the issue.
I deleted just the profile today, not the items and saves. However, when I try to download my profile I now get error code 80070525 and statement Live Profiles can't be downloaded right now.
Literally right before I deleted my profile I was online and I had no issues connecting to Live.