That's a great question, and it's often raised as a criticism of the low-income measure. I guess I would answer by saying it's multi-faceted. The situation you described, going from year to year, does in fact happen when you look at the statistics on a year-over-year basis. The low-income rate under the LIM doesn't always rise on the onset of a recession such as the 2008 crisis.
From a year-to-year perspective, it's often a good idea to look at other measures as well, such as the LICO, which are fixed in real values over time.
However, over a longer term, the measures that Statistics Canada uses are all relative low-income measures, so it's important to keep in mind that the concept of low income here is a relative one. A person in low income in 2014 should have about the same relative standard of living as a person in low income in 1990, say. Under a low-income rate that's fixed for a long period of time, that would not be the case.