To delete a scene you have to do it through the settings area. From home press Menu->Settings->Personalize->Scenes. Long press on the scenes in the my scenes area to delete or rename them.
Not sure on the not scene not sticking when restarting the phone. One thing that may be it that I have noticed is that if you change anything on any of your 7 homescreens (add/remove a widget or shortcut, change position of anything, change background, etc.) it does not update your custom scene but rather change to be a new unsaved custom scene called "Current (Unsaved)" In order to update your saved one you then have to resave with the same name, kind of awkward. I have noticed that if I don't save and restart my phone I get some strange results for the scene on restart, perhaps this is what is happening for you. Before restart, hit menu->Scenes and see if your current is saved or not.