Customary dropdown attic stairs are not designed for energy efficiency, and concerns like yours are extremely common. As those springs stretch, ceilings also settle. As a result, you get lots of air leakage - not to mention a noticeably uneven ceiling plane.
One solution is to ignore the sagging factor and install what known as an attic stair insulator. It's essentially an insulated cover that sits on top of the attic stair area. You have to remove it every time go up into attic, but the attic stair insulator helps energy efficiency by blocking that attic air from seeping into your living space, and vice versa.
Another option is a type of stair that's distinctly different, called a Rainbow Attic Stair. Rainbow Attic Stairs have steel frames that bolt to the door opening and are impossible to twist. The stairs come down telescope style - in other words, they don't unfold. The door that closes underneath it - the hatch - seals incredibly well. I went with this option when I improved the efficiency of my own attic last year. Standard dropdown attic stairs go for about $300, whereas the Rainbow Attic Stair cost close to $1000 after insulation. However, it's the last attic stair I'll ever need, and I saw an immediate difference in my monthly energy bill.
If you go with either of these options, let us know how it works. Good luck!