Although slightly different from the original report, I found a way to reproduce a similar problem:
1 - Delete the user data associated with the project.
2 - Open project in EiffelStudio
3 - Right click on the run button
4 - Click Add
5 - Change the name to -gui
6 - Click Close and say yes to the dialog box that appears.
7 - Quit EiffelStudio
8 - Relaunch EiffelStudio et reopen the same project
9 - Right click on the run button
10 - The -gui profile is selected, and now add `-gui' as argument.
11 - Click Close and say yes to the dialog box that appears.
12 - Quit EiffelStudio
13 - Relaunch EiffelStudio et reopen the same project
14 - Right click on the run button
15 - Select the default profile
16 - Click Close (note that this time now dialog box appears to ask you to save).
17 - Quit EiffelStudio
18 - Relaunch EiffelStudio et reopen the same project
19 - Right click on the run button, you will see that the -gui profile is selected instead of the default one.

Note that putting a breakpoint in `EB_DEBUGGING_OPTIONS_CONTROL'.load_dbg_options, at the line:
   l_profs := l_user_opts.profiles
I get 5 identical entries in it. This seems buggy to me, only one should be present.

In the original report, I lost the fact that I have -gui, but I believe it is pretty much the same kind of bugs.