What are some of the events that keep single mothers, specifically, in poverty?

This is a good example of what a cycle of poverty might look like. You can see that these events circle into one another and leave no room for escape. 

It starts with 

A: Poverty. This can begin from birth or at any point in one's life. 

B: Inadequate Diet. This is caused by poor nutrition along with poverty. The cheapest foods are the most unhealthy but also the most attainable (David Shipler, "The Working Poor" Chapter 8, Body and Mind).  

C: Poor Health. A direct subset of inadequate diet. This effects all aspects of live, especially when it starts from a young age. A lot of children suffer from poor health due to bad food choices and this effects their brain growth and can even mentally handicap them. Poor health also stems from not having the funds to get appropriate health care.

D: Low Productivity. This also follows suit to poor health. If someone is sick, not eating the right thing, and they have lost all motivation, they will often loose all moral towards working which can hurt them the most out of all of these. 

E:Low Income. Because there is the factor of low productivity this effects the income of the worker. They don't work as hard and end up not producing as much and that effects how much they are paid which narrows the chances of getting out of poverty even more. 

How does this effect single mothers?

These factors one by one effect single mothers immensely because they are often stressed and may not have the resources to feed their child(ren) the right foods. Which can potentially lead to a handicap, ADHD, and a slew of other issues that require extra work and time that these mothers just do not have. Being a single mother, they are already at a disadvantage within the workforce and in the world. They must be there for their children but also work sometimes multiple jobs to keep enough of an income to feed and house her children. Additionally if the children are younger, she must worry about childcare, one of the most expensive necessities. The odds are clearly stacked against a lot of these single mothers in the world