I have a M3, build 12/2018. Based on this or another post, I scheduled a mobile service call which I had this morning, to check the battery. Here is what the mobile tech said:
1. They don't bring a battery load tester. However, every time the car starts (when you first put your foot on the brake), it runs a diagnostic and will alert you on the Tesla screen if the battery has an issue. He indicated that you can't miss it. However, since this is only done when the car is about to be driven, it won't show up on the Tesla app.
2. With the old 12v lead acid batteries, it doesn't mean the battery will immediately fail and some people have driven up to a month with it with no problem, but you should use the car's notice as a reminder to get the battery checked and replaced. Part of this may be because the lead acid batteries are more powerful than the newer lithium ion batteries, but the newer lithium ion batteries may last longer. So, if you have the newer lithium ion battery, maybe make sure to get it checked when the car tells you there is a problem with the battery.
3. When a software update is available to be installed, the car will also automatically run the diagnostic to check the 12v battery as it needs that battery for the update, where the main battery will not be available. If based on that diagnostic, the 12v battery has a problem, it will notify you on the Tesla screen and will not install the update. However, he did not know whether this issue will also show up on the Tesla app. I am hoping that it would, since if the battery is ok, the Tesla app will show the update ready to be installed.