I've seen it happen many, many times. New Web writers accept very low paying work and then have to work an extreme amount of hours to make the money they need. Then, of course, there is no time to search for better paying work or to learn about other markets. All time becomes devoted to the low paying work in order to keep up the pace. People who get into this rut may never get themselves out.
Don't get me wrong- you certainly can't start at the top. Making the transition from print to Web writing usually means a learning curve and a lower wage to begin with. But, if it isn't going anywhere, it's time to overhaul your markets.
If you can't afford to stop writing for the low-paying markets long enough to apply to better markets, then simply integrate it into your writing schedule. Spend one hour per day scanning through freelance bidding sites. Also check out legitimate sites like ProBlogger and MediaBistro for better markets. There are many people who get high-paying work from Craigslist, but it is often much more time consuming to do so than to go elsewhere for work.
After integrating this into your daily work schedule, you will eventually see the ratio start to shift. At first 90 percent of your work could be in the .02-a-word ballpark, then 80 percent, then 70, etc. Getting out of the rut is possible, however. I have seen too many people lately who are stuck and see no way out. Just keep plugging away and in a few months the transformation will be breathtaking.