"Discharge Warning" not staying disabled

Not possible to turn it off without changing the programming in the ECM itself. The most you can do is turn it off and have it come back on restart. It's there because of the way the charging system works on the Kias (and many others) these days. Instead of the older constant charging at a lower amp level like the older cars the newer ones dump a lot of power into the battery soon after initial start-up and if the battery is discharged enough the high amp charge can damage the battery and the charging system.

Okay, if it's staying on while driving that is different than the common reason to turn it off IE; you want to listen to the radio with the engine off. On that system it only can be turned off on some of the earlier firmware versions, others it cannot. As you say it's been a while then that is a different issue.
If it's on while driving it is supposed to mean the battery isn't getting charged as fast as power is being taken from it. In that instance you cannot turn it off because it is detecting a constant fault. Same thing if the oil pump were to fail and turn on the light and shut off the engine, just not as fatal for the engine.
I would start by checking the actual charging system, a quick way for that is to use one of the free tests that some of the parts stores do. If it shows the charging system is okay (which is what I'm thinking the Kia folks found) then you test the sensor itself. First you will want to look as the AMS fuse to be sure it's okay, then check at the sensor for voltage and ground. The sensor reads the amount of power going into the battery and compares that with what the ECM thinks the car is using by using an inductive pickup that is part of the negative cable. It uses the LIN bus to talk to the ECM and determine if the numbers match. It replaces the old standard ammeter. In your case the sensor is sending data that says there is a higher drain on the battery than the alternator is producing. A quick test would be to use a voltmeter. First test the battery voltage with the engine off, a fully charged battery should read about 12.6-12.8 volts. Next start the engine and read the voltage now, if the alternator is charging the voltage should be around 14-15 volts and stay there for a minute then drop back to around 13 volts as it starts to cycle it on and off through the ECM. If you see those numbers the charging system is working, then test the sensors voltage. If those tests good, then the sensor is bad. However, one other item that can fail is the alternators overrun clutch. That isn't something you can test without the factory scan tool; its job is to act similar to the AC clutch and only power the alternator when required.

Replacing the sensor is easy to do. It is part of the ground cable clamp. You simply remove the battery negative clamp, then unplug the sensor, next unbolt the ground cable from the other side (green circled bolt). Reverse the process to install the replacement.

They still would have the sensor, but it likely only activates a warning light as the lower-level stereos don't use the LIN network. Antenna shouldn't do anything to the clock. The likely reason for it to lose settings would be where it gets the power feed to the memory in the radio and where it stores that info. About the only way to know for sure would be to map out the wiring to both units and see what is different, and what options are locked out through programming. For instance you can add fog lights to many vehicles that had them as an option, plug in all factory parts and they still will not work because the option code for fog lights isn't in the control module, because you didn't pay the extra for it. Could be a similar thing as well as the connections. With the modern rolling computers things like this are common.

Modern vehicles are a nightmare when it comes to adding things on. I've seen vehicles that started throwing odd codes because the aftermarket remote starter was sending bad data on the network, same with stereos and other add-ons. Even something like LED bulbs can cause problems in some vehicles and it's getting worse. Take a look at many of the vehicles that have large display screens instead of anything resembling a radio where everything is integrated in that one display.