"and on and on and on" is a way of exaggerating that someone or something does something a lot and/or repeatedly. In this case she keeps asking the same thing. "over and over and over" is another form of it and it means the same thing.

It means she was saying "Do I love you this much?" over and over, many more times than shown in the text.

Context: “Do I love you this much?’’ She’d ask us. Holding her hands six inches apart. “No,” we’d say,with sly simes. “Do I love you this much?” she’d ask again, and on and on and on, each time moving her hands farther apart. But she would never get there, no matter how wide she stretched her arms. This amount that she loved us was beyond her reach. Hi Lawrence, 1. The word "on" has the meaning of a continuous movement or action, and often, it is used to refer to the same repeated action. (Example: The dismissal bell rang, but the lecturer droned on and on.) 2. Therefore, when the lady asked "on and on and on", she repeated the same question, using the separation of her hands to symbolise the amount of love she has for her audience. In turn, as if on cue, her audience played along, and made her stretch her arms further and further to emphasise and acknowledge her great love for them. We see such dynamic interactions between close relationships where thoughts can be shared tacitly. "3. On and on" can also be used to describe the tiresome nature of something that is allowed to happen for prolonged periods of time. Example: Our failing marriage has been dragging on and on. Finally, we decided to file for divorce last May. Hope this helps. Cheers, Lance

'on and on and on' is very often used when someone talks too much. He talked on and on and on about his holiday. A colloquial version and very common phrase is 'he went on and on about his new car', ie. he talked too much about his new car.