Depend of the consequences. Sometimes, the attempt have severe result like brain injury, or other new affectations (like physical handicap when the attempt was launch from heights). Then, the approach to the illness have to change incorporating the new situation. In other times, with low consequences (only a pharmacologic intoxication), the result is the opportunity to reveal a hidden depression or the need to give a vital goal to the patient. But, always, the main consequence of a suicide attempt is the need to incorporate the death theme; and not only with the user, also with the families, professional and other user.
In my experience, a typical schizophrenic patient has no very much suicidal ideation. However, the initial schizophrenia sometimes has it. There are cases attempting suicide with confusion from slight auditory hallucination and hallucinosis. A few patients of the acute phase carry out suicide. The patient of schizophrenia of remission phase may think about suicide in a rather social environmental factor. Return to the society is difficult and sometimes feels despair. The issue of suicide of the patient of schizophrenia thinks that the early days and the timing of the comeback to social life are important.
The short answer is no-one knows. Suicidal thinking is common in the 'normal' population as well as schizophrenia, contrary to the above. Our 2010 review (see my publications) found suicide rate in SZ is 5%. If there is comorbid depression or substance abuse with schizophrenia this elevates risk of suicide & is treatable. Clozapine remains recommended in cases of SZ with suicide risk. Other risks (like being male) are less treatable..
Serious suicidal behavior, up to and including an attempt, may exacerbate symptoms and cause a relapse. In those with schizophrenia, or any serious mental illness, significant suicidality will negatively affect recovery. In those with a past attempt history it is possible that even suicidal ideation mat trigger retraumatization and raise risk. Developing/restoring strong social supports and connections should be part of any care plan. Clients should be helped to acquire coping skills to deal with the onset of any suicidal thoughts. Personal suicide prevention safety plans or a "WRAP" (Wellness Recovery Action Plan, see ME Copeland) are useful self-help resources. Peer supports such as a "warm line" should also be available.
My research thesis was on Study of suicide attempts in Schizophrenia. To answer precisely to the question you asked, a suicide attempt is the most important risk factor for further attempts during the course of the illness. The commonest cause for suicide attempt in schizophrenia is secondary to delusions and the second common reason being depression most commonly during recovery from acute phase or after gaining insight. Contrary to popular belief command hallucinations contribute to less than 5 % of attempts in schizophrenia. So based on the cause the dose of antipsychotics and adjuvant antidepressant, and psychotherapy plus family counselling should be tailored for better outcome