I think this might describe what you are talking about. I started searching the internet for this because I think I feel it too. Many people talk about how they feel sad about that they haven't done (enough) with their time or whatever. But I don't feel quite that way because I'm not comparing myself to someone else. I feel that it is a intense sadness knowing that you had something that will never be able to come back and that even now in this moment time continues and will never stop so all the things you have, even in the "right now", you are losing minute by minute and will not get back and there's nothing you can do to stop it.
Even though it is not the topic of the song, I think of the line from the song "Hard times come again no more"...."Let us pause in life's pleasures..."
or when I hear the slow version of Auld Lang Syne (Dougie MacLean)
I think this word linked above, applied to something or someplace comes pretty close. Chronophobia seems kind of close too but still seems just a little too general.