This is not an OS issue at all, because the wake-up should happen from **S5** (= power-off). Therefore, only the BIOS settings are of relevance. Since the BIOS settings have been working properly for quite a while I conclude there is a hardware-problem.
_Note1_ power-on is even instable using the power-button (I double-checked if the switch is defect, which it is not) so it has to be a hardware problem on the motherboard.