I've had a similar situation. My ex-T used to always ask to see my SI and ask questions. One day, she didn't. I thought she stopped caring or had given up on me. Next session, I sat in silence. She told me I could go because I was wasting both of our time. I broke down and told her my thoughts/feelings. Her response? That she trusted me to be honest with her if it was bad and I needed help. But she didn't want to keep focusing on the SI because she cared about me as a whole and not just someone who SI's. It was the first time I have ever felt truly understood and cared about.

Current T and Pdoc don't fuss much about the suicidal ideation. They trust me to be honest with them and to tell them when it starts getting bad. The main thing they worry about is if I SI again or if I'm not safe, that I won't tell them. But my T has come up with a system to easily clarify my moods:

10. Action
9. Desperation, withdrawal, not talking
8. Breakdown, crying, uncontrollable emotions
7. Severe depression, but no crying
6, 5, 4, 3, 2, and 1: I'm not at any risk.

My goal is to be at a 7 or lower. If at an 8 or 9, I need to contact her or call the police. We have a deal that I'm not allowed to act on anything until she responds, if I choose to call her in a crisis and not the police. She's only called the police on me once, but it was because I didn't pick up the phone after calling her in a crisis.

I think for anyone suffering from SI or suicidal thoughts that it is best to have a clear discussion about expectations and when/if additional care is needed. It will only help both the client and T trust each other more.