Re-rolling secured red/yellow dice in Elder Sign?
Yes.

The latest copy of the rules is actually much clearer than the version that came in my set. Here's the quote, with the same emphasis as the rulebook, but parenthetical bits removed: 


  When a die is secured on a Spell card, it remains there until any
  player chooses to use it to complete a task, removes it from the spell
  to roll it, or until another
  effect locks that die. For spells that
  secure multiple dice, the player may remove dice from it one at a time
  or all at once.