Self respect ?
Her kids getting confused at the conveyor belt of men coming and going ?
Her own issues about insecurity and being terrified of being alone ?
And probably a litany of other reasons ..
The kids know their mum and dad aren't together anymore so there are bound to be other people in their parent's lives, they don't appear to be affected by this at all.
How do you know she's terrified of being alone? If she was that terrified she'd have clung onto one of the other men