What version of Quicken are you running? In Quicken for Windows there is no “New Report” option, you are always customizing one of the standard reports.
When you customize one of the standard reports, it is saved under Reports > My Saved Reports & Graphs. This is clearer if you access the reports through Reports > Reports & Graphs Center, where reports you have saved are in the column at the right.
OK, I think I see what you are saying.
When you customize and save the Itemized Payees report, the Show Splits selection is not saved. I also see that the sections that were expanded or collapsed are not saved either. Is that it?
I do not have an issue where re-opening the report comes up blank, and for me the title of the report matches the name I saved it under, with the date range appended.
Also I see this is not a new problem. For example see here
https://community.quicken.com/discussion/comment/20047248