Why don't people who are suicidal seek help?

I was one of those people. It was too dark around me by the time I wanted to die, I had talked to people and tried to help myself, I had taken anti-depressants and tried self medication, psychiatrists, and counselors. Nothing helped enough to pull me out of it. I didn't care about the stigma and this was in the 70s and 80s when the stigma was significant. I didn't care about anything after a certain point. Medicine has improved a lot since then and so has the knowledge of depression. It is often a chemical imbalance that can be righted with medication but there's a lot of trial and error involved. I wish we had mental institutions again where we could treat people and make sure they recover under supervision but we don't. Read this, it perfectly describes the avalanche that is depression and I think it will answer some of your questions:

Good question. I think they are afraid, lonely, don't know who to seek help, even the closest person they are afraid of.

They are so depressed that they just think no one even cares.

Some does not want to know that they are weak and crumbling inside. I also wish that they will seek help. But acceptance and rejection is slways the thing there. Or they might not have the right person whom they can talk too

Sometimes they do, or have in the past, and they no longer feel that they can burden people with their issues (or at least that's what their brain is telling them). Sometimes asking for help results in being locked away for a period of time, and then released with no new solutions. It can feel scary and even dangerous to ask for help. Sometimes the brain is telling the person that nothing will work anymore, and it just needs to end. It's less stigma and more the feeling of hopelessness.

They often do but society doesn't always recognise their cry for help.

pride, and a sense that it would make them dependent on others - the very recognition of feeling helpless gets fuelled by having to ask for help and adds to the sense of despair - many do ummon help but sadly, many don't too

The reasons are as individual as the individual, just as the reasons for a person killing one's self is singular to that person. Yes, some people just don't get help. Others may "get help" but then never take their medications or go to follow-up appointments. Some just cannot escape the trauma of the past. Some just want the pain (be it physical or emotional) to stop. Mental issues -- especially depression -- aren't "A + B = C." My doctor told me there are tests that can determine exactly what type of SSRI a person needs tailored for their depression, based on genetics; however, the test is expensive and insurance won't cover it. And sadly, when "society" tells someone that their life isn't worth the cost of a test, there's not a whole hell of a lot you can do to counter that.

They ask Alfredo, most of the time they ask and very few are capable to offer help. Most of the time people say the wrong words.

I heard in church that someone else took their life, but no name was mentioned, so I don't know who. It's so sad. I don't know why people don't ask for help. Maybe they're afraid to.

In most cases, the individual had sought out help, yet it failed to keep their issues controlled. My daughter was in therapy, but nobody can change another person's mind-set. If they are determined to take their own life, sooner or later, they probably will

It's so expensive I think that's Why many don't seek help and some who can afford it don't want to admit they need help.

I think they do seek help. Maybe the people around them doesn't take it seriously because they know they are a strong person and could overcome it.

I think they are very afraid to seek help and are not very open to discuss their problems.

Sometimes people don't seek help because they believe that there is no hope. I once heard someone describe depression as "a cage without a key", and I think that depression leads to distorted thinking. I have had depressions for 20 years. When I am in the middle of a depression I am not thinking: "Things are bad right now, but they will get better" I am thinking: "Things are bad and they will remain that way forever." "I am a burden. The world would be a better place without me" is another example of distorted thinking and another reason why people don't seek help. Sometimes people didn't like the help they received in the past - medication with lots of side effects, nurses and psychiatrists who are too busy to talk etc and they stay away from help because of their low expectations.

Fear or maybe they are ashamed to let other people know about their issues.

That's very sad subject, I think there might be many reasons, and also big shame to admit something is wrong.

Some people ask for help and they are ignored.

Some do. But medications do not help. Society/system is not healthy for a human being.

Very true. It's a social stigma because of which many times people hesitate to take help because of the fear of embarassment and rather prefer to take their own lives which is so wrong. There is nothing in the world which is more precious than your own life and no such problem which can't be solved.