New, if it's under the roof line, it might just be too dry and not getting enough rain.
I would tend to bet that it's something in the soil left over from when they built the house. Might even be too high alk from the plaster/stucco.

Try a real tuff plant. If it were me I would try one of the small evergreen ficus like "green island ficus"

Here is a link that might be useful: {{gwi:987423}}

Those are tough areas. The experts say don't put mulch up against your house because it can bring in termites, so that's probably why the front bed was done that way in the first place.

I would go with native shrubs, because they can handle our summer downpours without rotting, and our winter dryness without shriveling up. There are a few I really like, I'm sure others will have some good ideas. But my favorites are:

Spanish stopper, it makes a nice narrow, upright shrub. You could try that behind the foxtails. It's slow growing, but exceptionally hardy. It will get tall in time.

Cocoplum, under the windows, also a really hardy native, with pretty, copper-colored new leaves. It doesn't get as tall as the stoppers and it keeps its shape well without a lot of pruning, which would be a pain behind the bed, up against the house.
Coontie, another slow-growing native that's really pretty, with a lovely mound shape, no pruning required at all. But they're sometimes hard to get started. Once started, they're gorgeous, and mine took off after the first year. But I have friends who have planted them and watched them die. So I think I was just lucky. Mine are in dappled, bright shade, and like it there, though I've also seen them in sun. I think starting them in sun might be harder. Coonties host a native butterfly that is in trouble, so they have that added benefit. And they are tidy, gorgeous plants when mature.

With the coonties, I've had a bug problem. I've battled them a couple times, there's a specific bug it and the gardenia get at the same time. I was able to rub and wash it off the coontie both times, but I've been told you can just cut them down to the ground _ once they're establshed - and they'll come back up bug-free. Don't even ask me about the blasted gardenia.

For some color in those beds, you might try some crotons. They're not really native, but they're pretty hardy and like our conditions. But, as Ricky as taught us, they're actually small trees and they don't really like to be pruned into shrubs. That said, I have a mixed hedge with several crotons in it that I love. Once their treeness begins to show, you can put plants under them to hide the trunks.

Have you thought about a rock garden for the south-facing area? I'm just filling one in now, so I'm no expert, but the advice I got here on GW was succulents and desert roses. I saw a gorgeous one at Fairchild that really inspired me.

If it's a soil problem because of the stucco/cbs, I've been advised here on GW to put my coffee grounds on it to amend the soil. That's kind of a chronic solution - ie, you'll have to keep doing it. But it definitely helps where the soil isn't acidic enough. You might try that near the back door (I'm assuming that's somewhere near your kitchen) and after awhile, you could try some kitchen herbs there.

As for the gutter guy, I agree, his advice is pretty suspicious. But maybe someone else here can explain what he's...

We had the same problem...'bout the only thing that will grow there is Bromelliads..They don't need soil,can handle the beating from the rain, and store water in their cups.

I think they are ugly, but they are green and cover the ground...and interesting when they bloom

I would suggest keeping that area cleared to allow access for maintenance (painting, etc). Some Floridians put down small white crushed rock. The previous owners of our house did the same only used red rocks on top of weed barrier.

You could put plants(bushes)farther out to hide the plant-free-zone and act as a green background with shorter ones in front. Probably just my personal bug-a-boo but I don't like plants right up against the foundation (termites, etc) as previously mentioned.

I will have to go with brick chips against the house instead of white crushed rock.Since you already have RED mulch the RED brick chips match it nicely and will blend in
If you really want to grow things dig out and replace some soil.Between the brick walk and house is a great place for mints and mediterreanian herbs.The mint should stay there.
But honestly your soil looks dead. You have a hose there so things will grow if you water and give them some nice rich soil. Unless you like cactus and crown of thorns but crotons should work also.

We have rocks along the house and was thankful for that when the termite guys had to treat this year, when the roofers came through a couple years ago, and will be thankful again when the painters come in a couple more years.

I have found that Fountain grass (purple and white), plumeria, Bird of Paradise (orange), crotons, and dracaena right at the outer eaves line will grow in small pockets created in the rock bed for them and still left enough room for maintenance. (We do have oversized eaves.) Each of those plants is fairly easy to contain size-wise for me.

For some of my more "precious" plants, I have sunk 20" or larger pots in the ground filled with good soil to plant them in.

Good luck in whatever you choose!