For me it is reasonable to demand that the T is:
On time for the vast majority of sessions.
Consistent about providing full sessions.
Patient and non judgemental.
Kind and considerate.
Professional, consistent and reliable.
Able to try to see things from your point of view.
Able to admit to their part in any 'ruptures'.

It is reasonable to ask an awful lot more of a T but they do not have to provide it and then it is up to the client to see if they wish to continue the professional relationship.
I have asked my T to see me twice a week, to allow me to contact her out of session, to sit close by me, to hold me, to play kids games with me, to colour in with me, to look after my rock and my bear for me, to hokd my hand, to tell me basic things about herself such as her age and favourite colour, clarify what of my list of things would and would not be OK between us, to give me her professional opinion on something that may be going on for me and more I am sure.

I am very grateful that she has met me on every one of these things that I ask of her and has said a few tines that nothing that I have brought so far is unmanageable. There may be a time but like Bay said, when and if that time does come I will look back and see that she has done everything that she feels is OK for us, that is good for me and this will make it much easier to see clearly the reasons for her not being able to meet what I ask for.

I am also lucky that I have never had to demand anything from her because she has provided all of the basics of being a T without prompt from me. This took me a while to be sure of and sometimes I still wobble but we are pretty much there.