As thesnowqueen said, this sort of thread is common, and seems awakening of attachment needs is the root of it. But i would argue that it's not just that, it's also the extreme rationing of contact. Therapy, in my view, sets up a cruel paradox -- activating of intense longing combined with long periods of separation broken only by contact that is brief and fraught with anxiety.

I think these scenarios where the client self-blames and self-pathologizes reflect the routine failure of therapists to inform clients up front that such behavior can result from the unique structure of therapy, and to explain what is really going. Might also be that therapists dont understand well enough to explain it or they are used to assuming that everything is about the client's preexisting issues. Context is important. Humans need proximity to attachment figures, therapy prevents it largely.

Does seem like OP might need more frequent sessions, but i think it's also relevant to ask whether it is healthy to be subjected to this dynamic at all, if it's triggering such preoccupation.