I don't know exactly what Starr did to progress his program with his trainees, but my guess is he had to start cycling in other rep ranges instead of 5s, which is what most coaches do now when they program HLM. Once you move to intermediate programming with something like HLM you will get the best results if you customize to the individual. For example a younger trainee could move from 5s to 3x3s on their H day, but an older client may need sets across of 5s and then greater reductions in the L and M days.
How long a trainee lasts in each phase will vary with age, sex, training history and consistency of training. Most people will be intermediates for the rest of their lives due to various interruptions (sickness, vacation, children, etc.) Pure weekly progression actually doesn't last very long for most people. At some point they will need a deload, which technically breaks the weekly progression. But if you are ignoring the deloads as a break, then this type of program can be run for months. I haven't had any clients training consistently enough to see if this can last for a year or more, but I suspect it would not unless they were young when they started.