The thing to keep in mind is there are two factors that affect rankings, internal = conversion rate/listing optimization/etc.. And external = promotions. To overtake competition, both need to be in check.
There are a few scenarios that could happen post any promotion.
A) Your listing moves up in rankings for the keywords you targeted and you "stick the landing". Your listing starts to convert searchers of those keywords into buyers and the organic sales you gain from the additional exposure keeps your listing on page 1.
B) You move up but fall back some degree. Maybe page 1 back to page 2. Page 2 to page 4. Your conversion rate is likely not on par with those ranked around your new position. Simply put. the listings around your listing are converting searchers into buyers better than your listing.
C) You don't move or move very little or even move down in rankings. This is typically a result of not allocating enough inventory per day for the keywords you targeted.
Example: If you want to rank for a very competitive keyword, like "vitamin c serum" and you allocate 10 units per day for 7 days for that keyword, you likely would not see an increase in keyword rankings.
If you have questions on how many units to target per keywords and other insight into your listing to have the best results from your promotion, get in touch with us about the listing and keywords in questions and we would be happy to assist our clients.