How many times can we recycle one sheet of paper?
Well apart from the fact that the answer depends on the type of the paper that is used. Secondly how much is wasted and also the process used. Below is an article that might be helpful in answering the question

Some industry sources estimate that an ordinary sheet of paper made from cellulose fibers derived from wood can survive only four to six trips through the recycling process. The Environmental Protection Agency puts the figure at five to seven times.
It is not surprising that the rigors of remanufacturing take a toll on the fibers.
Ideally, paper for recycling is separated into types, because paper with long fibers, like white office paper, offers the most flexibility for recycling, while newsprint, with its shorter fibers, is usually reserved for making more newsprint and other low-quality papers.
The paper is shredded and chopped, then subjected to a mixture of chemicals and water and heated as it is repulped. It is centrifuged and screened to remove impurities; de-inked with more chemicals; then sprayed onto a wire screen, drained, dried and squeezed through heated rollers.
With each step, the fibers become shorter, coarser and stiffer, so that eventually, recycled fiber needs to be mixed with virgin fiber to make paper of the desired quality.
According to the American Forest and Paper Association, 63.4 percent of the paper consumed in the United States was recovered for recycling in 2009. C. CLAIBORNE RAY

SOURCES: New York Times - http://www.nytimes.com/2010/12/21/science/21qna.html?_r=0