Why for the life of me I can’t stay awake when listening to Music?

Easy fix. Espresso and AC/DC.

Um, actually I'd suggest maybe you normally feel much more anxious than you realize.  Worth talking to an expert, but if you normally run with constant interruptions, from task to task, and then stop, then music is your signal to stop all that, but you are already overtired. 

The solution may be to find ways to be less wound up during the day.  Always, and I mean, always, reach out to a professional like a therapist who are really super nice and have a lot of tips you'd never think of. 

@OP If your system puts you to sleep at any time of the day, I'd get a health check.

If it makes you drowsy in the evening, that may just be the music putting you in a relaxed state and hastening you sleep - and nothing wrong with that at all.

Before the advent of screens, it used to be that reading or listening to relaxing music were normal pre-sleep routines.

Go see a doctor go through your list of meds make sure no reactions.get a sleep study you may be getting enough sleep time wise but not quality wise check thyroid labs tsh,t3,t4 and testosterone level  b12 vit d.  Best of luck.enjoy the music 

Niacin, Multi-V and Cawfee.  

https://www.youtube.com/watch?v=3gJd27E5X70