Most bloggers that get discouraged and decide to abandon their blogs tend to do so on the first three to six months. Sometimes the traffic is not growing as fast as they would like. Other times they are not happy with the money that they are making.
Personally I think that quitting after such a short period is a mistake.
There are two situations where quitting would be a smart move. One is when the blogger consciously decided to try out a new niche. In that case he must have some previous experience with blogs and websites, and he should know what numbers to expect and how to evaluate if this new blog has potential or not.
The other case refers to blogs that get stuck. If after six months you are still struggling to receive a couple hundred unique visitors daily then you probably are doing something wrong. Under this scenario you should probably stop to rethink your strategies (niche selection, content creation and promotion strategies) and try again.
On all other cases, however, the best idea is probably to hold tight and keep working hard until your blog or website achieves some critical mass. It does not matter how small or big your traffic is, as long as it is growing month after month you are on the right track.
The first three to six months are the hardest, and after that period you will notice that things will flow more smoothly, for several reasons.
First of all your content will achieve a bigger audience, improving the chances of receiving backlinks and traffic. Suppose two blogs, one with 200 daily unique visitors and the other with 2,000 daily unique visitors, publish the exact same article. The second one will have much higher chances of receiving backlinks, because more people will be exposed to its content.
This means that as your audience grow you will be able to spend less time promoting your content and more time actually producing it and making sure that it has quality.
Secondly, the credibility of your website will grow with the time, both for human visitors and search engines. Suppose again that two blogs, one that has been online for 1 year and has a Google PageRank of 5 and the other that has been online for 1 month and has a Google PageRank of 1, publish the exact same article. Even if we disregard the backlinks that each article will receive, the page of the first blog will appear first in the search results because that domain has more trust in the eyes of search engines.
These are just two examples of how allowing your blog to grow and mature will benefit you. The are several others: over the time it will be easier to monetize it, to get favors and support from your readers, to create a network of contacts, to receive freebies and so on.
If you are considering to quit, therefore, my advice is to hold tight a little longer, and then take that decision.