VERBATIMS

In general, what is the effect of price discounts on a brand's success?
Pricing shifts can generally spike purchases, but not create long-term value on their own
A strong brand can discount and not hurt their image--but a brand that lacks awareness & credibility ruins itself with discounting
Depends how you measure - equity or sales?
depends on the brands positioning
Depends on the product and target market (upscale product or me-too)
It depends--if discounting is a part of your brand identity, e.g. WalMart, then obviously it is positive.  If however you are Neiman Marcus, then it would have a negative effect.
it depends on the market, the product, and  the brand
It depends on the position of the brand--low price leader vs. premium
Price discounts can get the consumer's attention, but that alone won't keep it.
Price discounts may generate a short-term, temporary lift in product sales, but generally do not contribute in any meaningful way to a brand's success
Situational, in some cases, a high price immediately brings an association with better quality.
Sustainable Profit/Price ratio - make the same $ charge less.
The key is that price discount's drive the most traffic, but it negatively impacts the brand. My client has engaged in a series, almost perpetual series of discounts and they have diminshed what was a huge brand. The problem is that as a tactic, discounts drive traffic.
There is no way to answer this question in the absoute.  In some cases such as a restaurant client a discount may not have a negative effect on a brand's success.  In other cases such as a service, continuing discounts will have an adverse effect on that brand's success.