The easiest way to explain this to others (IMO) is as follows:
Continuous Traps, Continuous Spells and Equip Spells must be face-up on the field when their effect resolves, otherwise the effect disappears.
Which brings up one of my favorite "MST vs." situations ...
- Player A activates "Swords of Revealing Light"
- Player B chains to the activation with a set "Mystical Space Typhoon", targeting Player A's "Swords of Revealing Light"
"Swords of Revealing Light" is not a Continuous Spell. It's effect is not negated by virtue of being destroyed by "Mystical Space Typhoon". Any set monsters on Player B's side of the field are still going to be flipped face-up, even though Swords is gone ...
(oh, the debate I probably just opened up - lol)