It sounds like he prefers a set schedule as part of what you call the frame, so having the second session be a different day or time each week doesn't fit how he works. Part of it could be that it's also easier for him to schedule that way. It takes a lot of juggling to work with moving pieces all the time, and if all his other clients have standing appointments, it's less likely he's going to have a second appointment for you that's different every week.

I went twice a week for about a year and a half--same day's/times--and it really was ideal to have it set. I am now trying to work back in to twice a week every other week, between weekly appointments, and it's harder to find that second appointment, as it's dependent on someone else cancelling until a permanent slot opens up.

So I guess I get his point, having been through this.