Have you ever used an analogue signal for an interrupt service?
That the voltage can vary has no effect on triggering an interrupt. Any voltage above 60% of the reference voltage is HIGH. Any value below 60% is LOW.
The ONLY thing you should be doing in the ISR is noting that it happened. If the ISR is triggered at all, the Arduino will wake up and resume executing the statement after the one that bored it to tears (I mean that put it to sleep).
Since you don't have any code after that, loop() runs again, and you go right back to sleep.
You need to learn what you can, and what you can NOT do in an ISR, and don't do the things you can't.