As a kid, we had a summer home with rope weighted windows that were always breaking. My dad found a gadget that was similar to the drop-down door stops you often find on commercial doors. This thing had a rubber foot and counter-weight that you screwed to the sash, and when you raised the window its weight would force the foot against the jam and hold the window up. When you wanted to close the window you held the foot away from the jam and lowered it. You can probably still buy these gadgets in a store on Canal St in NYC!!
Another easier solution is to keep a thin stick (like a paint mixer) between the sash and the screen that holds up the sash as required.
Another idea might be to remove the sash and bend the springs to exert more pressure. You could also glue sandpaper strips inside the track to reduce friction. Something tacky like a little bit of dried rubber cement in the track might also work.
If all else fails, there are great vinyl replacement windows at reasonable prices that a DIY guy can install easily.