[NH.Solar]

This could also indicate a grub infestation. Are there any signs of skunks digging up the ground? Another way to tell is to grab a handful of the dead grass and give it a quick tug, if it comes up easily and there are little or no roots its probably grubs.
Have you checked the ph of the soil in that area? It wants to be somewhere around 6.5-7 and if it is wildly out of whack you are never going to be able to grow grass very well. NH soil is usually fairly acidic and correcting your ph is extremely important. Moss is an indicator of acid soil.
Lastly if you overseed be sure to buy good seed. Scotts has a really good special blend for our area called Northeast seed and if you mix that with their EZ Seed starter you will almost always get a good result. A lot of cheaper seeds have their balance of seed tuned more toward annual seeds rather than perennial seeds and this can also lead to what you have described. Annual seed comes up quickly and this can be useful to get grass to establish quickly but it doesn't renew very well. The EZ Seed starter mix has a lot of annual grass seed as well as the proper fertilizers and hormones to get grass established. The Northeast mix is mostly perennial seed, and when you mix the two you will get a result that comes up quickly and sticks around for the long run.
Cut your grass as tall as you can stand it and use a sharp blade. Taller grass means deeper roots and a lawn that can withstand a lot more stress. When you look at turf and think it needs cutting you aren't noticing the length of the grass, you are just seeing the uneven growth.
Finally when you water do so infrequently but thoroughly as this too will result in deeper roots and a much healthier lawn. If you have an irrigation system set it so it only comes on once every week, but do put down a couple inches of water.