If you are exppecting spectacular results in that lawn in such a short time it is no wonder that you are asking "what am I doing wrong" You are not doing anything wrong just expecting something that isn't likely to happen this fast.

From what I read here and elsewhere, milky spore can take years of repeated applications (every 6 months) to become an effective grub killer. I'm not sure why that is.

Was your soil damp when you applied the beneficial nematodes? Another pattern I seem to see on the Internet is that the milky spore works better in the north and the beneficial nematodes seem to work better in the south. I'm not sure why that would be but that's the way I read it.

Yes, my soil was damp before I applied the nematodes, and I watered them lightly after the application.
It seems to me that my lawn is looking worse and worse every year, and population of grabs is growing. I realize that it would take time to see same effects, but why does my lawn appear to be worse then 2 years ago?? Is the anything else I can do??

The biggest problem you have is your soil's pH.

You don't say what type of soil you have or where you're from but 25lbs/1k sq ft isn't nearly enough to bring your soil's pH up to where it needs to be. If you have a clay/loam type soil you've only applied about 1/4 what you need. Keep liming your soil at appropriate rates and intervals until it's near neutral. Your grass will be stronger and able to resist various stresses better.

Milky spore will also be most effective when the soil pH is near neutral as well. Warm temperatures and an active grub infestation are also important for success.

Here are some links that might help with milky spore. Japanese Beetle Grubs, Milky Spore for Japanese Beetles, Milky Spore Disease.

In reference to your soil test report.
What does the soil pH mean in relation to buffer pH? It is high in OM, so does that increase the buffer?

maplebirch, I'm not sure, but you might be right.

The pH of 5.2 is your active acidity. That is, a straight determination of how acid your soil is.
The buffer pH tells you how strongly your soil buffers against upward pH adjustments.
What they do in the lab is add an alkaline solution to your soil (the solution usually has a pH of 8.0). Then they re-check the active acidity. The more strongly buffered against pH changes your soil is, the lower that number will be.
For the grass itself, 5.5 or higher would be okay so the 25 lbs. might do it. Another 25 probably wouldn't hurt though. (to be quite honest, I have no idea the effect of pH on milky spore). Also, if you can core aerate prior to lime application, that will help move the lime down and adjust the soil pH throughout the active root zone more efficiently.
Your organic content is fine. Your phosphorous and iron are low. Potassium, calcium and magnesium look okay. Copper is low but, although it's in the literature, I've never seen a copper deficiency in turf.
On a side note, it's hard to tell from pictures, but the first two pictures look bone dry and the grass has the yellow/straw look that says "I could sure use a drink". Do you have sprinklers, and if so, how's your head to head coverage?
June/July when I started to notice yellow patches and tons of weeds.
Did you adjust your watering to account for higher temperatures and longer days?
I also see a tree there. What's the shade situation like? Does the grass perform better in sunny spots, shady spots, no difference?

Gargwarb, thank you for your explanation about pH. I've already added another 25lbs/1000 sf of lime.
In response to your question about sprinklers, I was watering every 3rd day for about 45-60 min. The amount of water was approximatelly inch per week.
The grass has southern exposure, and actually the grass in the shade is doing better than the one with complete exposure to the sun.

Gargwarb, thank you for your explanation about pH. I've already added another 25lbs/1000 sf of lime.
In response to your question about sprinklers, I was watering every 3rd day for about 45-60 min. The amount of water was approximatelly inch per week.
The grass has southern exposure, and actually the grass in the shade is doing better than the one with complete exposure to the sun.

That should be enough water with a well designed and properly functioning system. Is your water being applied evenly? I was leaning towards uneven watering before, and the fact that the grass is doing better in the shade has me leaning even in more in that direction. Here's a hypothetical scenario:
You have some spots that are getting less water than others. When temperatures are relatively cool in early spring, all of the grass does okay. When temperatures start heating up (June/July) evaporation, the water requirement of the grass, and heat stress increase. In relatively high water areas, there is enough water to compensate. In areas where water is low, but it's shady, that shade curbs the effects of increased heat and evaporation enough for the grass to survive. In areas where the grass gets the double whammy of relatively low water and increased heat and sunlight, it simply can't cope. Also consider the fact that if you have low-water areas, the grass in those spots won't develop as robust a root system and will have decreased capacity to take up water when the temperatures increase.
It's tough to tell from a couple of pictures on the internet but if it was my lawn I would be looking closely at my irrigation system. It would be a good idea to check for broken / plugged heads. You can also put some cups or cans that are all the same size out on the grass (some in the healthy spots and some in the not so healthy spots). Then turn on the sprinklers for a while. Afterwords, check to see if the amount of water you get in the cans or cups is even throughout the lawn.
I can't guarantee that poor coverage is the culprit but it's my suspicion. However, anything that stresses the grass can contribute to poor performance, such as the grubs you have there and the low phosphorous. Turf disease and soil compaction are also some possibilities to consider.

Thank you gargwarb, again,for your response. I think you might be right. My grass looks really good right now,( I'll take a pictures soon), after reseeding it in mid-September. I'll definitely take a look at the coverage area of my sprinkler system in the spring when I will restart them! How could I increase my phosphorous level in an organic way?? I do not think my soil is compacted though, because when I'm walking on it, I feel some softness under my feet.What kind of turf disease did you have in mind??

You can use bone meal for phosphorous. It comes in a bunch of different flavors. I would buy a bag and apply whatever amount you need to get about 1 to 1.5 lbs. of actual P per 1000 sq. ft. For example, if you find some that has a guaranteed analysis of 1-13-0, use 10 lbs. per 1000 sq. ft. followed by irrigation.
It's tough to tell if your soil is compacted or not by the way it feels when you walk on it. You might just be feeling the springiness of a thatch layer. To tell if your soil is compacted, try to stick a shovel into the soil and see how tough it is. If it's like trying to dig through a side walk, it's compacted. Of course, the most likely place to find compacted soil are in high traffic areas.
As far as diseases go, that's a really tough one to do over the internet. If you rule out everything else and you want to investigate the disease angle you usually need to have someone knowledgeable take a look at it, whether that means a site visit or you sending in a sample. If you end up exhausting the watering, nutrient and other cultural avenues and you still have a problem, your best bet is to contact your local extension office for more information concerning who in your area can help with turf disease diagnosis.

Thank you for the explanation of buffer pH. Just one more point of clarification. In the sentence:
"... Then they re-check the active acidity. The more strongly buffered against pH changes your soil is, the lower that number will be."

Does this mean that a buffer pH of 6.5 will be easier to change than a buffer pH of 5.9?
and Does that system hold true whether changing up or changing down?

Thank you.