I couldn't find a specific statement in the rules as to when the deck is reshuffled. In most game rules, even when the answer to this is simply "whenever exhausted" this is usually not assumed, but stated clearly in some relevant manner. However in this game, with the "Risk" mechanic, the deck can get down to a point where an attentive player will know for certain whether the last two remaining cards will match the symbol(s) sought, and so that leads me to wonder if perhaps the deck is meant to be reshuffled prior to the start of any "Risk" episode... Unless I am simply missing the relevant passage, the rulebook is mute either way.

When exhausted.

I question your assertion that an attentive player will know what's at the bottom of the deck.  I'm paying attention during the game, but I'm not counting cards.  This game is far too light to go to such trouble.  But even if I were a compulsive card counter, how would I account for the cards that are in players hands?

If you really feel this is a problem, here's a simpler suggestion to "fix" that without changing the game for anyone else.  Do all of your discards face-down.  When a player risks, he plays fae-up the cards he gets to keep and discards face-down the rest.