Personally, I think you should be able to have a Corrosive Surge+Burst weapon. That's just fine with me. I just don't see how it works by the listed rules without having to re-buy corrosive at some point (which can't work, because you already HAVE corrosive at the time in the form of acid burst).
I see your point, however, I have information to the contrary:
However, after adding a synergy property, the item loses its synergy prerequisite abilities.
Then.
A synergy property still counts as any of its synergy prerequisite properties for the purpose of qualifying an item for still more synergy properties. For example, a +1 acidic burst longsword is still considered a corrosive weapon for the purpose of qualifying to receive the energy surge synergy property.
Now, it counts for purposes of of qualifying, BUT it states that the item loses the item's weapon ability that is the prerequisite for the synergy. Now the Prerequisites for Acidic Burst, Energy Surge, and Earth Elemental power all list Corrosive. Not, Acidic Burst. Not Energy Surge. Just Corrosive.
So, as it reads:
1. Being Acidic Burst gets rid of corrosive.
2. Acidic Burst retains the corrosive WA, but only for the purpose of qualifying for another synergy.
3. Energy Surge gets rid of Corrosive, which has already been eliminated, but that doesn't matter.
I'm seeing this as a PrC that gives you a feat and states, "You don't need any of the prerequisites for this feat, you just qualify."
Acidic Burst comes with automatic qualification for Energy Surge. Just because it's telling you that you no longer can use Corrosive is fine. If I take two classes that say I'm illiterate, do I becomes Doubly Illiterate? If I take two classes that say I can't use armor, do I have to buy Armor Proficency just so I can lose it?
Synergies do not require the prereq as a PRICE. You don't PAY it. You still have corrosive in your weapon. Should Burst ever be dispelled and the rest of the sword's properties remain intact, the corrosive property still remains. You paid for it. It's in there, you just can't use it what you have a synergy in there.
I see from your use of the word "repurchase" that you think that the prereq is a price that is paid to buy the synergy. I see nothing anywhere to indicate this is the case.
To sum up:
Acidic Burst Qualifies Me For Energy Surge, and supresses Corrosive.
When I take Energy Surge, Energy Surge Only Supresses Corrosive, since that is the only weapon ability that it CAN suppress.