It's a possibility, yes. See, my wife (the sponsored person) did her 1st exam in December 2012. The exam results expired in Dec 2013, and because of that in Feb 2014 the CIC requested her to do another exam, which she did immediately. Soon she's expecting to get her visa and COPR, and we suspect that her COPR will be valid till Feb 2015 (which is 1 year since her latest exam).
However there have been cases when the CIC simply gave people an extension to the validity of their medical exam results. I'm not sure how they decide whether or not to provide an extension (if I remember correctly, if they expect to issue your visa within at most 15 months since the first medical exam, then they give an extension. But I'm not 100% sure about this).
But I do know that people who get an extension, usually have to land in Canada within a very short period of time. I've heard about people who had to land in Canada within 1 month, or even 2-3 weeks since receiving their COPR (that's crazy!) The plus side of that is they didn't have to spend more money to do the exam.
I personally would prefer to take the 2nd exam (rather than getting an extension) though. Yes it means spending more money for the exam, but that means getting 1 more year of validity, which gives you ample time to prepare for your departure, as opposed to having to depart abruptly.
I've heard about people who got an extension, had to land in Canada within 1 to 2 weeks, and because they didn't have enough time to pack their belongings, they ended up having to go back to their home country shortly after landing in Canada, pack the rest of their belongings, and go back again to Canada. LOL such a hassle.....(and costly too, due to the extra airfare =P)