Q:

Why wouldn’t they advance their technology?

After the apocalypse wipes out good chunk of humanity with atomic fire, people begin to form their own communities. But, a tribe in the ruins of Los Angeles has not advanced their technology in half a millennium, even though they have the ability to do so if they tried hard enough. The tribe's people are hunter gatherers, who use stone tools and wear animal skins. My question is, what would be a logical motivation for them not to advance their technology in such a long time, even though they could?
What the world is like
The Los Angeles ruins are full of many animals like deer, so the tribe has abundant food, and water is not a problem. The biggest threat to them are the screamers, a race of mutant creatures that often eat humans. They are very isolated from the rest of the world. The only outsiders they interact with are the occasional wanderers.

A:

To me, it is not surprising at all that a tribe does not invent.
There are different kinds of advancement:  perfecting and invention.
Perfecting:  taking something that is used and making incremental improvements.
Invention:  Creating something new to perform a new or old task.
It is likely that the tribe advances by perfecting current tools instead of inventing new ones.  Thus, arrowheads would get better and better over time but they would still be the pointy ends of arrows.  Most tribal cultures in the past had advanced this way until they were impacted by our "invention" culture.
Inventing, as we think of it, takes a pretty large population and free time.  For every new thing that works there are hundreds that don't.  A group that exists at a subsistence level just doesn't have the manpower or other resources to "waste" on inventing.  In the early days, inventors were generally seen as fools and dreamers that were wasting time when there was real work to be done.
This was true in our own culture until recently.  Just look at the British slang:  Boffin.

Boffin is a British slang term for a scientist, engineer, or other
  person engaged in technical or scientific research and development. A
  "boffin" was generally viewed by the regular services as odd, quirky
  or peculiar, though quite bright and essential to helping in the war
  effort. The World War II conception of boffins as war-winning
  researchers lends the term a more positive connotation than related
  terms such as nerd, egghead, geek or spod.

It wasn't until WWII that the word started to get a positive connotation.  That's not very long ago, all things considered.

A:

Technological advancement requires a broad infrastructure and stability (along with motivation, etc). Also it takes some smart people and, historically, a profit. These folks in LA don't have extreme weather to contend with so much of the motivation for creating power sources and refinement is absent. No furnaces, no metal work. (By the way, "stone tools", really? seems like there would still be plenty of refined metal around.)
 You say they are isolated so no trading partners so no profit or other incentive to create trade goods.
  Okay, I'm stuck on the "stone tools" thing. Even over a millenia there would be plenty of refined metals around LA. You know they make more than movies there, right? And a blast would have buried much material and even books (from 20th century).  
  LA is surrounded by desert (and cities in it) and things last a long time there. Not far away are clay ruins thousands of years old.    Even with some weird religion the threat from the Screamers would provoke them to using the best weapons they could. Without a Planet of the Apes virus scenario making people stupid as well as dumb you're gonna have Mad Max on steroids (LA number of cars and machines vs Australia). Are 90% of babies stillborn and this a ragtag team located...where?  
It would have to be a tiny area surrounded by hills that they never ventured from or climbed a hill and saw the remnants of vast civilization. Sure there's plenty of spots in southern California like that but not with potable water and sufficient wildlife; the primary inhabitants before people and cars was geckos. The current sighting of deer in the area is because deer are large rodents on stilts that live off people's gardens and agriculture and especially humans killing off the large predators, their natural enemies. More likely to have an increasing amount of predators such as cougars not to mention all the wild dog packs that would be inevitable.
   I can go with no ability to form a manufacturing base due to instability because of Screamers and lack of trading partners, information and education due to their isolation. And most of human history, about 10,000:1 , is people not developing technologically. That they haven't done it in 500 years is nothing.  
  The "cannibal" concept (accusation about the Screamers) is perhaps a good angle if they consider all meat to be cannibalism - perhaps a tenet formed after consuming tainted meat, perhaps because a memory of dogs as pets and since dogs are likely to be the most abundant wild animal in the area, this would preclude their consumption. Without another developed form of protein in their diet (and even bean growing takes somewhat advanced agriculture, irrigation - and cooking takes more tech, resources such as firecraft, wood, pottery) they would be mentally and physically stunted. Diet alone, especially after many generations, could explain the situation you desire.

A:

This has happened many times in human history. Advancing is done by a tiny minority of inventors who have the social power to make changes. The main demographic doesn't do anything. So plenty of societies never advanced for millenia outside their specialised way of life.
Hunter gatherers in Australia never advanced for possibly more than 50,000 years. There just wasn't a need and no one in power had that tiny spark of genius that led to agriculture elsewhere. Tribal societies are very different from democracies. People are usually tied by bloodlines to status. An inventor without status will be in trouble.
Another reason could be the elites suppress advancement for their own reasons and agendas as it will impact on their power and prestige, this happens right now almost everywhere in many fields.

