If you are receiving an error code with the diagnostics, then it means you have a hardware issue of some sort. It really is that simple. macOS & third party apps do not play any role when running the Apple Diagnostics since the diagnostics are booting to Apple's online servers & launching just the diagnostic app...no OS is loaded and only the diagnostic app is in memory.
If this laptop was under warranty a month ago when you had them examine the laptop, then I think you should be able to make a case today that the diagnostics are confirming the problem you reported previously. However, an AASP will not have the authority to make a repair exception....they would need to contact their Apple service contacts to allow the repair exception, but this is not easy for an AASP anymore especially if a month has elapsed. An Apple Store might be able to make the decision themselves since they are actually Apple.
You can try contacting Apple corporate to lodge your complaint to see if they will do anything for you since Apple online tech support is unlikely to do anything, although you could try.
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You can also check out your local consumer protection laws to see if any may apply or help you here.
Unfortunately most Apple techs seem to have only a very limited understanding of hardware troubleshooting if the posts on these forums are true. Most seem to only follow Apple's extremely basic & limited methods of troubleshooting which includes trusting in the Apple service diagnostics...unfortunately diagnostics rarely report any hardware issues. The best way for Apple to know you have a hardware issue is by performing a clean install of macOS which is where you first erase the drive followed by reinstalling macOS. It is important not to install any third party apps and not to restore from a backup since both of these things may bring back any software or configuration issues. If the issue occurs with a clean install under these conditions, then Apple should be replacing some hardware on the device. Receiving an Apple Diagnostic error code should also have Apple replacing some hardware. Of course they may not know exactly which part is actually bad, but at least they should be replacing something.
You neglected to mention the exact model of your Mac. There are some models where I won't recommend repair because they are known to have multiple known potential issues, or the model may be getting too old to warrant a repair. Some of it depends on how the laptop is being used, the software you require (if they need to be at the latest versions since some apps may not be able to be updated with some older versions of macOS such as 11.x Big Sur which just became the latest casualty depending on the apps needed), and personal finances. Generally I wont recommend a repair for 2019 and earlier models. 2020 MBPros.....not a big fan of them either, but some of that is just my own personal opinion from supporting thousands of my organization's Macs.
The general rule is if a repair exceeds half the cost of a replacement laptop, then it is usually best to invest in the newer laptop.
Hopefully you can convince Apple to honor the warranty if it only expired a month ago and you have documentation showing you reported the same issue to them while under warranty. Apple should have notes in their system about the previous examination even if you don't have a copy.
Good luck.
