You are not providing enough information for anyone to answer your question.
What type of appeal are you talking about?
What did the underlying action involve, from which you filed an appeal.
Why do you think that you have the right to file another appeal?
What court dismissed the appeal?
I agree with Mr. Larrimore. The question is particularly impossible to answer because it is unclear whether by "second appeal" you mean "reconsideration" or "review by the next highest appellate court in the state." It is not even clear whether you are in state or federal court. Some states do not have more than one appellate court (e.g., West Virginia) so there would no opportunity for a "second appeal." You will have to provide far more information in order for anyone to provide you with a meaningful response.
The appellate record needs to be examined because what is in the record already sets the stage for what can be done next. The answer to your question may take several hours of legal research. You do not state what the outcome was. Why? And to decide what the next step will be needs to be really fast because the appeal deadline clock is running
You might find helpful my Legal Guide Questions to Consider Before Bringing an Appeal
No one can know what the record is in the case because online we cannot see your documents. You need a lawyer. Check with a lawyer in your locale to discuss more of the details.
Good luck to you.
NOTE: This answer is made available by the lawyer for educational purposes only. By using or participating in this site you understand that there is no attorney client privilege between you and the attorney responding. This site should not be used as a substitute for competent legal advice from a licensed professional attorney with whom you have established an attorney client relationship and all the privileges that relationship provides. The law changes frequently and varies from jurisdiction to jurisdiction. The information and materials provided are general in nature, and may not apply to a specific factual or legal circumstance described in the question.