This may seem like beating a dead horse, but you must remember always that your article must serve it's primary audience: the reader. If you don't care about the reader, it will show. Don't get caught up only in getting links back to your site.
Be aware that not all article directories will accept your content automatically. Follow their guidelines and specifications, which, most likely, will include the requirement that your article be well-written and informative.
In addition, if your article provides value to readers, it will more likely be picked up by other publishers. Write the articles that publishers want in their publications and your potential audience will exponentially grow.
Your article is going to be published online. This means people will only find it if it relates to the key words and phrase they are using to search the web. Therefore, your article needs use key words and phrases strategically. Be very careful not to overdo this -- keyword stuffing is bad - don't do it.
Once the article is found, it must be read or the the reader will not make it to your resource box and click through to your website. So make your content good and your resource box compelling.
Also, you need to be strategic about the article you publish. Create a plan for your article marketing so that you will know what you are doing, why and when.
You publish articles to article directories for three basic reasons: branding, lead generation and promotion. But there is only one reason to write an article, and that is to inform your audience. If the article is not focused on this primary and most important purpose, it will fail to achieve the three reasons you're publishing the article because no one will be interested in reading it.
First and foremost, you need to get people to read your article, then make them click on your resource box. This is achieved by writing quality content.
I know people who submit articles three to five times a week. These folks are usually using article marketing to support their affiliate marketing efforts. In this case, volume can make a big difference.
I believe that once a week to once a month is sufficient for steady, organic traffic growth in most cases. But, of course, the more articles you post to directories the better.
To "win" the article marketing race, quantity is quite important. So, posting more often will help you reach large numbers more quickly.
Ultimately, the question you should be asking is, "How does article marketing fit within my overall business strategy?". Your answer to this question will help you decide how often you should be posting.
Are you using article marketing to improve off-page SEO through back links? Are you using it to drive traffic to your site? Are you using it to prime your list-building pump? Each of these goals will be facilitated by a slightly different strategy.
I don't think there is any article directory rule that limits how many articles you can submit at one time. That said, if the resource box is pointing to the same website for each article, I would limit it to two or three. You want to build your back links in a more organic manner and suddenly having 50 back links to your site from one directory may get you dinged for content spam by the search engines.