It is a requirement for inland that you are in Canada. If you leave, even on a short trip and for some reason are refused entry to come back, your application is gone.
Instead of leaving and coming back, you can extend your visitor status by applying for it, see
http://www.cic.gc.ca/english/visit/extend-stay.aspAs long as you apply before your status expires, you would be under implied status and allowed to stay even if you haven't received an answer yet at the time of expiry.
The processing time for first stage approval is now 11-12 months on average, see
http://www.cic.gc.ca/english/information/times/perm-fc.aspAt the time of your first stage approval, you will be granted an open work permit if you have applied for one. If you didn't apply with your sponsorship package, you will have to wait until you have your first stage approval. You can also use the form to extend your status to apply for your open work permit when that time comes or you can apply online. You can find the form here:
http://www.cic.gc.ca/english/information/applications/visitor.aspEven with a first stage approval and a work permit, it is still a requirement that you reside in Canada so again, if you leave and for some reason aren't allowed back in, you would lose your application.
Your partner leaving Canada should not affect your application. He is not moving to another country, just going away on business for a month here and there.