Why arent mosquitoes found near neem trees?
The growing accumulation of experience demonstrates that neem products work by intervening at several stages of an insect's life. The ingredients from this tree approximate the shape and structure of hormones vital to the lives of insects (not to mention some other invertebrates and even some microbes). The bodies of these insects absorb the neem compounds as if they were the real hormones, but this only blocks their endocrine systems. The resulting deep-seated behavioral and physiological aberrations leave the insects so confused in brain and body that they cannot reproduce and their populations plummet.


In case of a regular (house) mosquito, the effects of neem are as follows:
1. Retardation of growth
2. Inhibition of feeding
3. Eggs are unable to hatch

Apart from this, larvae of a number of mosquito species are sensitive to neem. They stop feeding (as mentioned above) and die within 24 hours after treatment. 

Studies regarding your question are still in process so it's hard to narrow down to one exact reason.

Sources referred: The National Academies Press