Why does Online Dominion allow you to reveal reaction cards multiple times?
Yes, you can reveal a reaction drawn by Secret Chamber.  For example, the following scenario is perfectly valid (according to BGG's Dominion FAQ)


Be attacked.
Reveal Secret Chamber.
Draw two cards (one Moat), replace two cards.
Reveal Moat to deflect attack.
Reveal Secret Chamber again.
Draw two cards, replace two cards (put Moat back on deck)


Most reaction cards, such as Moat, have no real value to being revealed multiple times during the same trigger.  However, since the rules do not explicitly forbid such behaviour and there may be other edge cases where revealing the same card multiple times has merit, it remains a valid option.