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When we took the site on, the first, most important keyword had the site around position 8 on page 1. A few days later, it had dropped to the bottom of page 5 for this term. We have been doing various onsite work and building links via directories and article sites and this has now risen to position 5 on page 4.
However, with the second keywork (the less searched term), the site was and has remained page 1, position 1.
Is it possible we could be penalized for one search term and not the other? If we had been penalized, surely the site would have dropped for both search terms?
What other factors can cause such a dramatic drop off for one key word and not the other?
These 2 other sites bring very very little revenue, revenue that he wouldn't miss. Should we 301 these sites to the main site?
regarding the recent movement in search results, you might want to follow the relevant (current and previous) Google Search threads:
Google Updates and SERP Changes - July 2009 - part 2 [webmasterworld.com]
Correct. If both keyphrases are equally competitive and one falls but the other remains then chances are there hasn't been a penalty.
"What other factors can cause such a dramatic drop off for one key word and not the other?"
It could be many things. The duplicate content issue seems most likely.
I find it rather odd that the client didn't give you the full picture when you took over the project, you had to discover an additional mirror site on your own. Maybe the client has a few more secrets, like some linking scheme that he disassembled so you couldn't find it hence the SERP plumeting or maybe it's something else. The next time you sit down with the client see if you can get more information about his previous web site promotion strategies, you may find you answers there. If it is something real bad, it may take some time (4-6 months or more) to regain credibility with the SE.