Hi Fran,
Though it's definitely another classic song of the early sixties, I don't think "All Alone Am I" is the song Steve is refering to, because Brenda Lee's song lyric does not actually include the phrase "every beat of my heart" in it. She sings "just the beat of my heart" and "just the lonely beating of my heart".

"All Alone Am I" lyrics:

All alone am I ever since your goodbye
All alone with just the beat of my heart
People all around but I don't hear a sound
Just the lonely beating of my heart

No use in holding other hands
For I'd be holding only emptiness
No use in kissing other lips
For I'd be thinking just of your caress

All alone am I ever since your goodbye
All alone with just the beat of my heart
People all around but I don't hear a sound
Just the lonely beating of my heart

No other voice can say the words
My heart must hear to ever sing again
The words you used to whisper low
No other love can ever bring again.

All alone am I ever since your goodbye
All alone with just the beat of my heart
People all around but I don't hear a sound
Just the lonely beating of my heart

Scott