If I encounter a travelling pokémon, is it gone forever?
Solution 1:
Typically, they won't disappear, unless you do the stupid option of restarting the game, making everything disappear. Another way to prove this is how sometimes Pokemon are on missions different than yours, in which the 'closed' icon appears instead of the Pokemon. After a small while, they'll come back. This is typically the same as those you encounter in the dungeon to refill your HP, PP, and belly.