I know that grass has fairly good shade tolerance, but....."mainly shade a very little sun"= Dead grass.

Any way you could trim some trees to get a little more sun to it? It could be fertilizer burn or to much water in your shady areas. Cut back on watering to 1 time a week and see what happens. Try to get more sun to the grass.

That sounds like more of an over0watering issue. The shade may have some role in it, in the sense it is not drying out the soil but the shade itself *in SoCal* is probably not what the rest of us on the E.coast are thinking of when we think of shade.
Cut back your watering and try again. You can let the soil dry out and try to water as infrequently as possible, some people advise even waiting until the first signs of stress before turning the sprinklers on.

Well a few things could be going on. I have a few questions for you. Try to be specific as possible.

1. Have you submitted a soil test recently? (Checks for PH, Nutrient levels, organic matter etc.)

2. How much sun does the grass receive? (1-2hours, 1/2 day, filtered, etc)

3. How old is the grass?

4. At what height is your mower set to?

5. Have you fertilized? if so with what and how much?

6. Can you take and post some pics?

I think I can summarize exactly the cause of your dilemma.....compaction.

Your soil where the lawn mats and you say dies, is very compacted. This usually happens more easily where clay soil prevents water retention. Traffic....never-ending walking on...causing a path in reality...is compressing the soil, it has no chance of absorbing nutritives and any water just runs away.

If you can aerate properly....and that is with a machine you can rent at rent-alls, then do that.
If you cant afford such fix, then the least you should do is next spring.....that's pretty soon isn't it in California...get out your stiff rake, and rake hard over the area. What grass you remove shouldn't be there in the first place...that is the stuff that dies.
Open the pores of the soil.

Rake hard, first in a north/south direction.....then go back and rake hard in west/east direction.

Then topdress with 1/2" of topsoil or compost that is crumbly....doesn't hide the grass. Then overseed the area with your choice of grass seed for your local conditions.

Then use watering practices that brings about the grass.

Aeration though sounds like your salvation...it will remove cores and open up the soil for better penetration of mositure and fertilizer. It sounds though like this fix-up might apply to your whole lawn area....not just the one where traffic has caused the problem.

I always have to go look up these grass varieties. Marathon, for those of you who don't know, is TTTF. And for those of you who don't know what means, turf-type tall fescue is a grass that does spread by itself but the progress is measured in terms of ice ages. Basically if you want more grass, you need more seed/sod. I have seen it everywhere in SoCal. It does seem to do surprisingly well even in the very dry climates of the desert. I guess they water the heck out of it. I have also seen it choke, cough, and sputter in even partial shade. It could be that it just won't work in your shade.

I am experimenting with a type of zoysia called Shadow Turf in my yard. It is a fairly aggressive form of zoysia. It filled in very quickly after an initial 2-month period where it spent its energy sending out rhizomes instead of green tops. Then suddenly I had it everywhere. My application has much (MUCH) more sun than I anticipated (we removed a tree), so the grass is doing extremely well. I have also seen it in an application ranging from full sun to no sun under an English walnut tree. It looked incredible everywhere except in the no-sun area. There, after two years of trying to get established, it is still trying. At least the grass is winning, just at a much slower pace. The one-inch plug is now 1 square foot of dense grass after 2 seasons. But elsewhere it is very plush, dense, and a very nice color of green. This grass is surprising me. They said it was shade tolerant, but this is more than tolerant.

Where in SoCal do you live? I don't need the nearest two intersections but the name of the city/town would help pin you down. For example if you lived in Blythe the suggestions might be different than if you lived in Big Bear or Newport.

you are over watering it. what gardening zone do you live in?

Here is a link that might be useful: lawn care

You gotta give us some more info because people are just guessing now. eg watering 2-3 times a week with a misting isn't the same as a good soaking. Also, do you have a sprinkler system or just a hose?