I'm an E5 at a Big Tech company. A Director in a different org previously mentored me with weekly 1:1s, then tapered them off to every 3 weeks after he helped me through a major issue. Then he got swamped with hiring and onboarding managers in his org, so he often skipped our scheduled 1:1s. It was hard to predict whether he would show up or not because he would usually accept the calendar invite. I would only find out after I pinged him ~10 min into the 30 min 1:1 that he couldn't make it because he would sometimes join the 1:1s when I pinged him.
One time, another 1:1 ran over and I prioritized that over this Director's 1:1 since I didn't know if he would show up or not. As luck would have it, this Director pinged me several minutes into the 1:1 and asked if I was joining. He seemed offended when I asked if we could reschedule because my other 1:1 ran over. Did I violate some etiquette around 1:1s? When I told him that I can't tell if he'll show up to our 1:1s or not, he said, "They're just standing 1:1s." Could someone please explain to me what that means, especially the etiquette rules for it?
There are no rules... You have to stand up for yourself sometimes and not subject yourself to the whims of the person right above you in the org chart. You deserve to feel a sense of dignity and if you feel like you're being disrespected, tell them that although you are grateful for their time, you must also have some autonomy/ownership of yours. I don't know if ending the 1:1s is appropriate since they're only once every 3 weeks.
I like Michael's answer a lot -- it's fine to reschedule a 1:1 meeting in good faith and not feel guilty about it (especially if you've only done it once).
However, the fact of the matter is that there likely is a power dynamic here. The director is likely busier than you (as an E5), and perhaps they perceive the "opportunity cost" of a no-show on a meeting to be a higher.
In general, I really dislike when people cancel meetings a few minutes before they're about to happen. A few tactics to prevent this from happening:
The reality of the situation is as you get higher and higher in level scheduling becomes more and more of an issue. I wish I could show you the ridiculousness of my outlook calendar. I often have triple and quadruple booked time slots and I have to make a judgement call about who I'll let down. It sounds like your director is prioritizing his own time over your convenience but you should understand that you need him more than he needs you and his calendar is likely a circus like mine is.
I am allergic to reoccurring 1-1s. My philosophy is the optimal time to meet mentors/mentees is on-demand because the necessity of the discussion is likely not going to be evenly distributed across time. When you had major issues to work through he had no problems meeting weekly. When things stabilized the urgency left and his prioritization shifted.
My recommendation is to proactively cancel meetings when there's nothing urgent to talk about. For weeks there is something meaty to talk about, I would recommend that you update the meetings agenda to reflect the value and urgency of the conversation that you'd like to have so he has a reason to shift his priorities around.