I've been through Cave 2 a bunch of times, and I almost always leave between runs. I've never had any problem with Yamina - the additional attempt missions are at the bottom of her list, below the options to start brand new missions.
These are clearly missing from your screenshot, so I can see your problem, but wanted you to know it does seem to work. I often have leftover attempts for multiple caves ongoing, without issue.
One time I got disconnected during a Cave 1 run. I logged back inside the instance, but I only had one run left at the end, when I expected two. I wasn't 100% sure if it was my first run at the time, so I let it go, but I wonder if that could have been an issue.
Hope this case is resolved soon.
Cheers,
Miles