My heart almost failed me when I saw the school.

It does not mean the heart has "failed" or stopped working.

When the boy's heart had failed, the father promised to follow Him if the boy lived.

I listened to its song, and my heart failed me.

For a moment, his heart failed him when he actually saw a plane in the distance - then another.

My heart failed me when I thought of the blood.

The man who died, he said, was 80 years old and his heart had failed.

Perhaps his heart might have failed him in the dark days to come had he not been so.

Or what if his heart failed on this ride and he died with me?

His new heart failed him after six years and he died in Toronto.