Could I continue in my preferred field whilst working on a post-doc in a different field? I am coming to the end of my present post-doc position which is in a fairly narrow area, one that I am deeply interested in pursuing further.  I am struggling to find a new role in the same area.  

What are the implications for someone in this position when i) taking up an unrelated post-doc role, or ii) working in industry until a suitable role comes up?

Some good answers so far, but I would like to extend my original question to:
iii) What are the implications were I to accept a role working in field A, and continue to publish work in field B.  I assume in this instance I would naturally discuss this and only proceed if my primary investigator were happy with it, for example, but could there be other implications/considerations?
There are many whom I know have done their post-docs in a field far different from their primary area of research and work. I don't see this as a problem. Post-docs and PhD dissertation may also widely differ from person to person. I have not seen such a phenomenon affecting their career.