Psychodynamic therapy does place a high value on consistency. I can understand your therapist thinking that standing appointments on the same days and times are ideal for both sessions--I feel like since going to two sessions a week I notice any departures from the normal schedule even more, and like the solid routine of predictably timed therapy is more important than it was once-weekly. I'm not an extremely routine-bound person in general, but therapy is more productive for me when I'm able to have a consistent, predictable rhythm with scheduling.

So I agree that predictable twice weekly is better than an unpredictably scheduled second appointment, but that doesn't mean that consistent/predictable once weekly is better than an unpredictably scheduled second appointment. My sessions definitely move around sometimes because of conflicts on both my end and my therapist's, and I'd always much rather reschedule but still have two sessions than just cancel one outright. Maybe your therapist would be willing to give things a trial run with adding second appointments as you're able?