This article should help to answer your question:

http://www.pnas.org/content/early/2008/12/01/0803408105

But in short, mosquitoes are able to combat infection of viruses such as Dengue and Chikungunya by the production of virus-derived small interfering RNAs (viRNAs). The reason that strain C6/36 die when incubated with viruses is due to the suppression of these viRNAs (link below):

http://journals.plos.org/plosntds/article?id=10.1371/journal.pntd.0000856

Mosquitoes do get affected from virus attacks I have studied on Aedes aegypti if mosquitoes are made infected by dengue viruses their egg laying capacity goes down. 

The incubation period , the amount of virus initially taken up by mosquitoes and the susceptibility status also plays role in virus development rate in mosquitoes in cell line there is no defencse system when one cell is destroyed whereas in mosquitoes it has some defence system and variety of cell types which differentially develo

Although it was widely believed that vector-borne parasites should evolve to be benign towards their invertebrate host as they are dependent on their survival for transmission, a number of recent studies have found that infection with vector-borne parasites often reduces the fitness of the invertebrate vector. I have posted below a great review on this subject.

http://rspb.royalsocietypublishing.org/content/276/1660/1369.long

With regard to dengue studies have shown that there may be a fitness cost associated with dengue virus infection, I have posted a recent paper, that contains relevant citations within.

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0059933