I have friends and have talked to other parents, who have enrolled their students in K12 and they have complained about this same issue.
I can't speak for all the Connections Academies, as different states vary in laws and requirements, but I can tell you that Ohio Connections Academy is very flexible when it comes to live lessons, at least at the elementary level. (My son will be entering middle school this year.) From Kindergarten to 4th grade, the students have math and language arts live lessons. In Kindergarten, my son had two a week -- one math and one language arts. As he got older the number increased.. by 4th grade, he had math live lessons every day and language arts live lessons twice a week. In Ohio, live lessons are not mandatory, but students are encouraged to attend as many as possible. The live lessons are always recorded so if your student misses a live lesson, he or she can watch the recording when time allows. In 5th grade, students have math live lessons every day, language arts live lessons twice a week, with a writing live lesson once a week, and science once a week. Students are required to have contact with their teacher at least once every two weeks, this comes in the form of attending live lessons and their monthly phone call. I have found Ohio Connections Academy to be extremely flexible. My son did not attend every live lesson and he did very well. We also have a nontraditional school schedule. My son does school work Friday - Tuesday and has Wednesdays and Thursdays off. We've had this schedule for five years and it has never been an issue.