Need Advice: Appeal or Reapply

My wife recently had her visa application for a family visit turned down because she did not declare her previous passport which has been missing for some time now. The old passport had been used for a previous application also for a visit to the uk about 3 years back which was turned down because her sponsor had been the sponsor of several other applications. Our country commenced issuing new types of passports in the period after the misplacement of the old one so she got a new one. We had not reported the loss of the old passport because we still believed it was misplaced during her move from her previous work location, to lagos and we that we may still find it. On her visa application which asked if she had a previous passport she indicated no and also indicated that she had not be declined a visa application before. Answering otherwise required providing details of the missing passport and the previous visa application which she could not provide because of the loss of the old passport, this was why she answered No to both the questions.

The reason for her current visit is to attend her sister's wedding which comes up in March. Her other family members who applied for the same reason have been granted visas, so it looks like she is going to be the only one to miss the wedding which is quite devastating to her, weddings are a big thing here.

Should she appeal explaining the reason for her filling the application the way she did and apologise for the incorrect information she gave or should she reapply? If she appeals, what are her chances and what are the chances of its being resolved before the wedding in March. Should she reapply immediately and take her chances on whether the new application will be granted when she fills the form correctly, should she also attach an apology to the application? Is there a minimum waiting time before you can reapply? I would like to have this cleared up, so this incident does not besmirch her immigration record.