That's a good questions, and to be honest I'm not entirely sure myself. I think when I first translated it I assumed that "息を止め" or what I've translated as "my breath stops" (but could maybe possibly be translated as "Stop, breath" or "Stop your breathing", since the subject isn't clearly stated -- often the problem when translating from Japanese to English) wasn't literal. So I was thinking more along the lines of a separation of love perhaps. And the singer is trying to see the meaning in moving forward while reconciling his lingering feelings and thoughts for his love.
But as you've mentioned, it could be the separation of death if that "breath stops" line IS literal. That seems like a valid interpretation too. I don't really know which is more correct!