Hcfyk

The Vanguard Style feat states :

While using this style, when an adjacent ally is required to make a Reflex saving throw, you can expend a use of an attack of opportunity to attempt the aid another action to improve your ally’s Reflex save. Your ally gains a +2 bonus to all Reflex saves while adjacent to you until the beginning of your next turn.

Unlike other effects based on attacks of opportunity and the aid another action, like Bodyguard, the target keeps the bonus until the vanguard's next turn beginning.

This bonus seems to be untyped and as stated about the Aid Another action in combat :

Multiple characters can aid the same friend, and similar bonuses stack.

Does that mean that if an ally of a character using the Vanguard Style is required to make several Reflex saving throws during the same round, the user of the Vanguard Style can use it each time (with enough attacks of opportunity available) and, each time, the ally will obtain a cumulative +2 bonus on its Reflex save ?

I can't find anything wrong with this reasoning but the result seems rather strong to me, especially if a build improving the aid another bonuses is involved.

No, it cannot stack with itself

Bonuses from the same source (feat, spell, class ability, racial ability, etc) will never stack with themselves, as clarified in the definition of Bonus:

Bonuses are numerical values that are added to checks and statistical scores. Most bonuses have a type, and as a general rule, bonuses of the same type are not cumulative (do not “stack”)—only the greater bonus granted applies.

The important aspect of bonus types is that two bonuses of the same type don’t generally stack. With the exception of dodge bonuses, most circumstance bonuses, and racial bonuses, only the better bonus of a given type works. Bonuses without a type always stack, unless they are from the same source.

So, using the same feat twice will not grant it's bonus twice. Similarly, using the spell Bull's Strength twice (even if two different casters do it) will not grant a total of +8 to Strength.

Unless said ability specifically says that it stacks, but those are rare. For example, the Fleet feat.

As for being strong or not, I would rather not suggest allowing an exception and trust (with a grain of salt) that the developer who wrote it to decide if the feat balanced or not. There are feats with similar effects that call that they stack, and a bunch of Aid Another(-ish) type feats that do not stack, and the benefit of this feat is granting an ally the benefits of another feat for one round (Lightning Reflexes) which seems balanced (to me) for a feat. Especially if you consider that despite the requirement, you are not actually required to use a heavy shield (it could be a tower shield), and you could grant the Vanguard Style bonus to multiple allies against a single area attack.