With U-verse you most certainly do have such a piece of equipment. The
NVG510 is a dual-purpose device; it's both a router and an ADSL/ADSL2 bridge ("DSL modem").
The router portion of the device is literally intercepting your browsing traffic to tell you that there are problems with your DSL line quality, and makes (bad) assumptions that it's related to the lack of a DSL filter on other lines in your house (e.g. telephones need to be plugged into filters, which then plug into the wall).
In my experience, however, the issue usually turns out to be with line quality between the outside of your home (or apartment) and the actual DSLAM at either the CO (central office) or RT (remote terminal). This manifests itself as bad signal-to-noise ratio ("noise margin" or "SN margin") or power levels ("line attenuation"). It's usually the result of some tech out in the field fucking around with wiring (rewiring portions of the area in a bad manner) or damaging existing wiring. It could also be caused by environmental factors. Sometimes its related to the time of day (often at night, when things like city lights turn on and cause noise/interference which affect copper wiring). It can also be caused by distance from the CO or RT, which can sometimes change if engineers screw with area topology wiring (e.g. you were previously 4000 feet from the CO, but now due to a topology change, you're 120000 feet from the CO). AT&T should be able to rectify all of this, but it may take them weeks or months.
You can see all these levels within the device itself; there is an administrative interface on the router which has a page that
looks something like this. Don't ask me how to get there, but the device has this information. The information is lost once you power cycle or reboot the device, so you will need to periodically take snapshots of it yourself.
Rebooting the device doesn't actually solve the problem, it just temporarily works around it. Sometimes slower network speeds get negotiated in this situation (slower speeds allow for less strict signal/power levels), and it'll work until the line quality improves briefly, a new (faster) speed gets negotiated, until things degrade again, rinse lather repeat.
If you Google the error message you'll find tons of people reporting this issue. It's all related to line quality.
Bottom line: contact AT&T and make them send techs out to test line quality. They have the tools which can do this, and can tell you what the problem is. They can usually figure out
where the issue is, but you need to put pressure on them to do their job. They can also (very very easily) rule out inside wiring problems (i.e. issues in your home/apartment).
I recommend when engaging AT&T, you begin keeping a very well-written diary of every event. Dates, times, what transpires, names of individuals, callback numbers, managers names/numbers, etc.. Log everything. If your issue doesn't get fixed, you can continue to put pressure on the company and all of those individuals until it does get fixed. Be friendly/courteous, but get every single person's name and number, including that of techs who you meet in person. Trust me, if it turns out to be a bigger issue, you will need this information.
I myself had to do something very similar to this with Comcast, and it took nearly 5 months to get the issue resolved (turned out to be 2 sections of damaged wiring between utility poles which were accepting interference from nearby cellular LTE towers which used the same frequency range as Comcast's service (~700-770MHz)). You can
read my story if you want (long, but worth a read if you're interested). I still to this day believe the only thing that lit a fire under their ass was me calling back one of their "supervisors" after many months stating that I was at my wit's end and was considering writing a letter to Comcast's CEO and my local city hall regarding the negligence (specifically because this affected a small area of my city, not just me personally).
But most importantly: there is nothing anyone here on this forum can do to rectify your problem. You need to talk to AT&T.
Good luck.