With any offshore development (using any methodology) your biggest hit in productivity comes from time zone differences and impeded communication.
The lack of synchronicity in working hours usually induces high latency in response times (one persons comes in for work while the other one is already finishing up, discovers a problem and then has to wait until the remote person gets back to work to have it resolved, etc.)
High latency is especially problematic with agile methodologies as these methodologies rely on immediate, person to person communication. High latency also arises from less immediate forms of communication usually used with offshore development - emails, scheduled conference calls.
To mitigate, I would recommend:
A. Rely more on immediate forms of communications - IM, VOIP, person to person video teleconferencing. Consider having a webcam based teleconferencing system in each project room that is 'always on' and allows for more coherence between the two parts of the team.
B. See if you can create more overlap in working hours by moving each part of the team's working hours 30 minutes to one hour closer to the other. This would buy you an hour to two hours of extra overlap in working hours.
In general, however, I believe agile methodologies (capital-A Agile, SCRUM, XP) work better for offshoring than classic SDLC methodologies as the team's ability to respond quickly to changes that may result from cultural/technical misunderstanding is better.