I assume you're talking about child benefits of some kind such as SSI or Survivor Benefits. Yes, you can ABSOLUTELY keep receiving benefits while homeschooling. My father died when I was 12, and I am physically disabled (legally blind). I started homeschooling when I was 14, in 9th grade, and continued until several months after I turned 18 (my birthday was in September, so I, too, was still in school at 18 (it isn't uncommon, people, really). I was receiving survivor's benefits at the time, and before SSA would continue sending the check past my 18th birthday was if I proved that I was still "in school". This, however, did not mean in a public or private or online school. They wanted some kind of proof that I was being homeschooled. We live in Florida, and in our state, when you register to homeschool, the school board will send you a letter of acknowledgement at the beginning of every year for just such an occasion. The letter simply states that I am being homeschooled legally by my mother for the current year. We simply sent this letter to SSA, and they continued to send my SS benefits.
If you're in a state that doesn't send out letters like this, you can send some kind of letter from your homeschool co-op, a letter or transcript from an online school, or a letter and transcript from your mother. The best thing to do would be to call your local Social Security office and ask them what they would like to see from you before they continue your benefits.