Can someone please recommend a good firm or contractor for writing and maintaining an online product manual in English?
I had a good experience with the Documentation Doctor
http://www.documentationdoctor.com/ I helped me with the creation of the manual for my text expansion software Direct Access.
Hope this helps.
Oleg, You may want to try to scout technical writers on Odesk or Freelancer. If your product is highly technical, or complex, you may want to write the technical manual yourself and then hire a good editor to edit your document. This will save you some money, probably make it go quicker, and the editor will bring a 2nd set of fresh eyes to your documentation.