I let SimulIDE to save the open asm file with a new name. Running the debugger again, the Debugger didn't forget the breakpoint locations. This is not an issue.
The issue is that, after running the debugger for the new/renamed asm, there were no more yellow squares at these locations, and it wasn't possible to deselect them too!
Also, by just deleting the *.brk file and re-starting the debugger, the situation didn't change. SimulIDE had to be exited and re-started to remove these breakpoints.
Off Topic: (a practical suggestion)
Is it possible printing the header of a process, like 'Loading hex file:' for example, right after clicking its 'Upload' icon?
I guess, this is just more practical than printing it at the end of the process.
Another example is to also print 'something' right after clicking on the 'Debug' icon.