U-verse reboots every morning at 1:00 a.m.

This is not normal for U-verse.  Some nights it might reboot for a firmware update; not every night.  You have some other issue going on.  Try using Smart Home Manager app in your phone as soon as it goes out and let it see the problem and create a trouble ticket for you.

Same thing happens to us. It occurs between 1030p and 1 am. Most times it is between 12:50am and 1am. I do check the smarthome
manager and nothing registers. I believe it is related to updates but when I call for support to ask about it. Support doesn’t know and wants to send someone out. They have been out, replaced modem, dvr, checked wiring and can’t find anything wrong so they claim it is my tv which it is not.  I believe this is being caused by AT&T  or something related to U-verse. Their support (Edited per community guidelines) because they offshore support and just follow script and not trained .they spend hours on the phone going in circles instead of actually fixing the problem. When requesting Manager assistance. It takes another 45 minutes of asking if they did anything wrong . 

MIne reboots the TV at exactly 1:01 AM and around 4:00 to 5:00 AM every day.  It's irritating as (Edited per community guidelines), if I'm watching a show, at that those times.  It's been that way for 8 years, two different modems.

Thank you. That makes sense. Unfortunately, Transparency is not AT&T’s forte. Even as recently as in the last week, the same issue has been reported but all they do is their scripted support which does NOT do anything but waste time and money. Their technical support and customer service support go silent when I suggest that something, on their end, is triggering an automated reboot daily. Then, they get defensive and try to shift the blame to the customer. For example, maybe the cat (we don’t have one) jumped on the wires and loosened them for example. Or maybe we need an extender or maybe technical support should come out again. Or, maybe there are too many things connected (nope… 2-3). 
bottom line is that AT&T claims they claim they don’t know what is causing it. If there is an automatic reboot or refresh ( which I believe there is), let the customer know.

Smart manager shows that the network is up while this is happening. I do notice the speed slow down, almost like it is being throttled during that timeframe.

Gateways do not normally reboot every night.  If yours is doing that, it is out of the norm.  Yes, AT&T may update the firmware on your Gateway, causing it to reboot, but that happens about every 3 months, not every night.  So, yes, it is probably something in your home or at least specific to your connection, not AT&T remotely rebooting your Gateway.

Do you have fiber or VDSL2/ADSL2+?

I do notice the speed slow down, almost like it is being throttled during that timeframe.

If your gateway is rebooting, how are you passing traffic at all.  Perhaps you're not having the same problem as the other people in this thread?