It may be to do with the particular kind of grass, the soil and how it's been cut.
For example, in the UK, a lawn made of soft-grass, cut rarely, would be very floppy when walked on.
On the other hand, a lawn of, say, rye-grass and fescue, mown once a week, would be tough, springy and hard-wearing.
There are people who make a career out of making good lawns...
Where are you? What kind of lawn is it? What has been done to it?
An autumn lawn feed will improve the strength of the grass but I'm pretty sure your grass does stand up again after a little while. It's the grass flattened by a roller or mower with a roller that gives the stripes btw. When it stands up the stripes disappear