Note: Posting as an answer on Mark's suggestion
Indeed, the deals of ViaRail unfortunately only cover a few itineraries, and usually only between major stops.
There are few ways to get a good deal with ViaRail. The main one I know of, for cross-country tourism, is the Canrailpass. It allows you to travel for 21 days and/or 7 one-way trips (whichever comes first). The pass costs from $630 to $1100 (plus tax)
In your case, the trip from Winnipeg to Churchill (round-trip) is worth $300-370 when bought at full price.
As I suppose you don't live in Winnipeg, you can also use the train to get there. It is purely hypothetical, but then, a round-trip from Toronto is worth over $400, and the pass becomes pretty competitive. Especially as you will probably visit Churchill in low season (I heard best time is around end of October), so the pass price is comparable to the round-trip price from Toronto, so you can add some free train rides to your agenda.
To add a bit about the pass conditions : you are allowed 1 stopover for each of the 7 one-way trips. With the pass, you can only have access to seats with supersaver/discounted fares, so book ahead (but you can cancel any trip before train departure).