I haven't had a problem with the grass going flat and I mow high. I think it may happen more when the grass is young. I'd try dropping the deck a notch and see if that helps. If not, drop it another notch. Mow it that way for a while, then raise it a notch to see if it stands up straight again. If you dropped it two notches, leave it raised one notch for a couple of mows, then raise it again.

Do you know what variety of grass you have? Some of the fescues will fall right over when they are tall.

If Kentucky Bluegrass is fed too much Nitrogen it can tend to lay over, what is known as lodging in grain fields. The grass stems are too weak to support the grass.

The grass seed I used was mostly tall fescue. Not the best quality, home depot special.

Will it correct itself as it matures?

"The grass seed I used was mostly tall fescue. Not the best quality, home depot special.

Will it correct itself as it matures?"

No amount of time turns crappy seed into good grass unfortunately.

so there's nothing I can do? Will overseeding in the fall help with a good quality seed?