A game like "raze" that is on Steam?

Then instead of looking for another game, we should find a solution to the problem. Check to see if the browser doesn't delete cookies or cache, or if you have an antivirus, I'd check there as well. Also, right click on the game screen, then Settings. Let the webpage store unlimited information.

Also, there just might be a way to keep the game directly on your computer, but I don't know if it would save the game as well...

That would be to:

1. Go on the webpage where the game is being hosted (in this case, http://armorgames.com/play/5395/raze).
2. Wait until the game is FULLY loaded.
3. Click on the webpage anywhere (but not on the game screen).
4. Click "Save Page As..."
5. Save it in a folder (Personally, I create a new folder onto my desktop).
6. Open the folder you saved it in. You'll see a webpage shortcut and a folder. Open the folder, and like for a .sfw file (should be called raze-5395.sfw).
7. If you have a program that runs .sfw files, double click on that file. Other wise, open a browser window, then drag and drop the .sfw file onto that window.

You can then enjoy playing the game without the use of the internet... Only, I have no idea whether your game will be saved or not. You can only try. :P

"The game is normally played in a small map with +- 10 players (bots, because it's a singleplayer game)" I didn't saw in the OP that he's actually looking for a MP game, but rather for a side scroller where you aim with your mouse