I have absolutely no idea how this discussion has become so long. It seems HorusMaster is arguing one thing (that Rainbow Veil carries on negating throughout the game if it and the negated monster stay face-up on the field), and everyone else is disagreeing with him.
I certainly agree with the majority, for the reason that it's smegging obvious. Horus, man, you're stretching it too far. (And for the record, I've never before said "man" like that.)
# "Rainbow Veil's" effect starts being applied when the attack is declared. It does not start a Chain. It does not target the opponent's monster.
# Effects that activate in the Graveyard or removed zone will not be negated by "Rainbow Veil".
# If a monster affected by "Rainbow Veil" is not destroyed by the battle, its effects remain negated for the remainder of the Battle Phase.
# When "Rainbow Veil" is removed from the field or negated, the effects of the monster you battled with are no longer negated.
# If a monster equipped with "Rainbow Veil" attacks a face-down monster, when that monster is flipped face-up in the Damage Step its effects are negated.
# If a monster affected by "Rainbow Veil" is flipped face-down after the battle, its effects are no longer negated.
# While "Rainbow Veil" is equipped to a monster that is unaffected by the effects of Spell Cards, "Rainbow Veil's" effect is still applied.
There's the rulings. I've emboldened one, look. The one that refers to a SINGULAR Battle Phase.
There's no evidence at all to suggest that it applies even in all subsequent Battle Phases. Yes, it becomes active when the attack is declared, that's fine. And the effect stops being active at the end of the current Battle Phase. Also fine. But the negation
doesn't become activate again at the start of the next Battle Phase (even though the rulings don't say that - Note that more importantly they don't say that the negation effect DOES become active again, negating the old monster).
Once you hit the end of the Battle Phase, there's nothing at all to worry about (no remembering which monsters were attacked, etc.). The next Battle Phase will be started completely irrespective of what happened previously. A monster equipped with Rainbow Veil, when it attacks something, that something will have its effect negated for the rest of this Battle Phase, and ONLY for THIS Battle Phase. That's what the text says.
Rainbow Veil's effect applies to everything the equipped monster attacks, but ONLY for the Battle Phase in which it was attacked.
There are many similar effects, such as the aforementioned Steamroid and Crystal Beast Topaz Tiger. Exactly the same wording, but we know their ATK boosts/losses don't stack. There's no reason at all to suspect Rainbow Veil works any differently. And indeed, it doesn't.
You might just consider dropping this, Horus, and accepting how it works. You're straining yourself to read the text slightly differently to match what you apparently want it to say.
If you have any examples of a card with similar wording that follows your thinking, please state them. When you do so, try to explain why Steamroid and Crystal Beast Topaz Tiger do NOT follow your thinking. If you have no examples, you're arguing for a precedent that goes completely opposite to the similarly-worded cards already existing, which is illogical.
EDIT: Okay, perhaps I've been misinterpreting you, Horus. Sorry.