Official Ruling
No, you can't. This effect is triggered "when a card is removed from your opponent's security stack," so even when you check multiple cards in your opponent's security stack, it is triggered and activates upon the first check. Also, this is a [Once Per Turn] effect, so this effect activates when a card is removed from their security stack upon the first check, and you can't activate the effect again upon the next check.
Source: BT16-013 Valkyrimon ACE