Tell us a bit more about the version of LightBurn, and under which OS? What device profile have you selected, and do you have more that one created?
Save Positions are a Device Profile level setting, not file level. I am not seeing what you describe. Running the latest release, I can View, Select, Go to, Manage, Edit, and Delete these position settings without issue, so we are going to need more to try and track what you are observing.
Edit: Save Positions are a Device Profile level setting, it wouldn’t make sense to store a position for a different laser of a different size (might be out of bounds).
We will continue to poke around, but cannot reproduce this issue here. Please check, click the Devices button to see if you have more than one defined. Any other settings not saving? They all save in the same file. Please share anything you can think of, the exact steps you take to reproduce this issue, and we will continue to try on our end as well.