Final answer:
The patient's neurological deterioration is likely due to opportunistic infections like cryptococcal meningitis or HIV-associated dementia, which are common in late-stage AIDS when the CD4+ T-cell count is very low.
Step-by-step explanation:
The neurological deterioration in a patient with candida esophagitis and a CD4+ T-lymphocyte count < 200/mm3 is likely caused by opportunistic infections or conditions that affect the nervous system, such as cryptococcal meningitis or HIV-associated dementia. These conditions are common in the late stages of AIDS, where the immune system is severely compromised. Given the low CD4+ T-cell count, the patient's immune system cannot effectively combat infections, making them particularly vulnerable to neurological opportunistic infections that can lead to severe complications or even death.