Thanks!
Sorry my typo, I meant December page rank. October PageRank was also 0, which was not unexpected since the website had just been launched last April. However, it was a surprise to us it was still 0 in December, after we had got a number of good backlinks.
As I mentioned earlier, organic search traffic has been increasing steadily since October even for the homepage that was loosing rankings. However, most of the increase was probably due to low-tail keywords. I cannot see how anyone would be going to page 6 of search results.
I'll follow your advice on examining the competition in more detail. However, it still seems the problem is deeper than that.