I think it does depend on your definition of crisis, as Chris says. I began therapy suicidally depressed and would occasionally relapse into suicidal thoughts for quite a while. I would say that my T would work hard to prevent crises and to help mitigate those when the occurred, including encouraging me to call and calling me back and spending quite a bit of time on the phone with me sometimes.
In terms of our relationship, however, he will wait for me to bring up issues between us and will not broach the subject himself. Well, once, he asked me about a feeling of coolness and distance he was getting from me, to check in to see if the feeling was accurate. He asked if I wanted to discuss it and I did. Other than that one instance, he has waited for me to bring it up. When I ask him why he doesn't bring things up, he mentioned that once he thought what he was sensing was just me trying for some emotional space and wanted to give me that. Once it was to encourage me to develop healthy interpersonal skills. He has admitted that on a couple of occasions he did not bring up the discomfort between us because he had his own personal anxieties about the subject and didn't really want to talk about it.

He quickly followed up on that by saying that he DID want to talk about it because I needed to, he was just trying to explain that he was anxious about it also and that why he avoided the subject until I brought it up. He then commented on my "courage" in being able and willing to bring it and address it head-on the way we needed to.