Have you talked to your T about this? About how you feel?
And, have you also considered, that perhaps it's your perception, rather than the reality, that your T seems so distant? That is not to say it is your 'fault' or that your feelings are not valid - they are, because they are your feelings - but that this might be the area you need to work on in therapy, with your T, with the focus being on your response, rather than the relationship with your T itself.
Have you felt this way before? Has this 'feeling distant' happened in other relationships you have had? Ie, you entree a relationship in which things go well for a period of time, and then you start to feel the other person is 'distant'?
You have every right to feel hurt / afraid of why your T shows up late - that would upset me greatly, I would take it personally for sure. However - can you see you instantly decided it was because of something YOU did? Maybe it was something in the Ts life that made them late - maybe they had another client in crisis, or were late due to traffic? If their being late was due to another client, its not likely your T would say that was the reason *although some might).
More importantly, why other 'evidence' is there that the relationship has disintegrated? That is a very strong term to use if the evidence is that your T has been late a few times; so it leaves me asking 'what else is going on?'
On a similar note, is it possible you have had previous experiences with being let down, not liked, felt others have rejected you, or that you have 'down something' to 'make them not like you anymore'? If so, then it's more likely you are experiencing transference with your T. It might be your T just happened to be late, BUT, due to your previous hurtful experiences, in your mind, it is PROOF that your T no longer likes you and is distancing themselves from you.