It means "I can't avoid thinking that..."
for example have a look at below
The scars of your love, remind me of us.
They keep me thinking that we almost had it all
The scars of your love, they leave me breathless
I can't help feeling...
It means "I can't avoid thinking that..."
Here it is referring to the next line. She keeps thinking that they could have had it all. It means it seems obvious to her that they could have "had it all", been happy and together for life.