The simulator is designed to clear itself after you close the browser window - this helps prevent endlessly looping mods and slow loading times.
One way I can think of is just to make your own mod in the mod.learntomod.com/programs section.
Press Blockly multiplayer (not singleplayer), and create a main function (make sure it says main), then go from there. Make sure you don't have any blocks floating outside of functions.
You can build structures this way (see the Drone badges on how). You can also use the schematics tool on the learntomod homepage and add a schematics block to the mod. Remember, some blocks are too advanced for the simulator to render, but you should be able to create structures using any blocks show in the main badge tutorials (though not necessarily the quizzes).
So whenever you enter your simulator world, you can just load that particular mod and press the m button.