Female mosquitoes require blood to produce eggs and can feed up to three times as much as males, its is only females that feed on blood. There is no limit to how many time a single mosquito can bite you. If a mosquito feeds but is interrupted before it has had enough, it will bite again until full. Once satiated with blood, the mosquito will rest for two to three days before laying its eggs and beginning its search for more food - and more mosquito bites. Therefore, an individual mosquito may bite as many times as desired in order to get what it needs.
Not all mosquito species mate and lay eggs more than once; those that only do so will likely only bite once. However, mosquito species that mate more than once tend to bite much more frequently as they need the blood for nourishment in order to survive.