What maladaptive behaviours or cognitive distortions develop as a result of chronic childhood illness? It's fairly well documented that childhood trauma (such as chronic illness) can lay the neurochemical groundwork for conditions like depression later in life. A paper, "The link between childhood trauma and depression: insights from HPA axis studies in humans", states:


  We here summarize results from a series of clinical studies suggesting that childhood trauma in humans is associated with sensitization of the neuroendocrine stress response, glucocorticoid resistance, increased central corticotropin-releasing factor (CRF) activity, immune activation, and reduced hippocampal volume, closely paralleling several of the neuroendocrine features of depression. Neuroendocrine changes secondary to early-life stress likely reflect risk to develop depression in response to stress, potentially due to failure of a connected neural circuitry implicated in emotional, neuroendocrine and autonomic control to compensate in response to challenge.


"Late Consequences of Pediatric Chronic Illness" has some related findings too.

I'm interested in what psychological groundwork might be also laid by early life stress such as childhood illness, also contributing to the development of mental health conditions. For example, I've read of cases where chronic childhood pain may cause the patient to have an unhealthily high acceptance (not tolerance) of stress as an adult, meaning they persist in stressful situations where others would not. They've learned that pain is to be accepted and worked through to an extent beyond which many would think reasonable, and this may lead to stress related illness.

Are there any other maladaptive behaviours, cognitive distortions or similar that commonly occur in adults who experienced chronic childhood illness?

(Also interested in evidence related to my anecdotal example.)

EDIT (31st Dec 2013): Thanks to caseyr547 for his answer. To clarify, I'm particularly interested in answers using the behavioural, cognitive and psychodynamic models, as opposed to the biological or stress-vulnerability models.
There are many psychological models for abnormal behavior so there are many ways to answer your question.
The Stress-Vulnerability model of mental illness is a well established biological theory. It states that biology provides from vulnerabilities to mental illnesses which are activated by stress and trauma. It would dictate that the stress/anxiety caused in the past and present by a bad childhood could result in any mental illness based on what biological vulnerabilities were present in the person. 

I think you should read "Chronic childhood disease: An introduction to psychological theory and research", "The occurrence of maladaptive health-related behaviors and teacher-rated conduct problems in children of chronic low back pain patients" and "Abnormal illness behaviour: childhood experiences and long-term consequences", "Relating Parent and Family Functioning to the Psychological Adjustment of Children with Chronic Health Conditions: What Have We Learned? What Do We Need To Know?"