You can always apply but you might just see the same decision. The reason is that one an I-130 is filed in your behalf there is an immigrant intent which is difficult to overcome.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.
By having PR parents and an I130 filed on your behalf is prima facie evidence of immigrant intent. Consult an attorney
Yes, you may apply again, but unless you cure what was the basis for the first denial(s) you are likely to receive the same response. In your case, because of your LPR parents, it appears that this fact is seen as evidence that you harbor an immigrant intent, i.e. you yourself will want to immigrate to the U.S. since your parents already have. This is in contradiction to the purposes of the visitor visa, which may be why it was denied. To optimize your chances of being able to travel to the U.S., consult an immigration attorney.
This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.