You should not. There is an appeals process established by the Social Security Administration that you should use to appeal denied claims. Where appeals are concerned, however, you only have a certain amount of time to file them. If you wait over 60 days to file an appeal then you do need to file a new application.
Expect to be denied initially and when it’s reconsidered. You may have to go to hearing to get it approved. The appeals process, however, is there to give you a chance to argue your case. If you wait the 60 days and apply again, your claim will most likely be denied for the reasons that got it denied in the first place. If you keep filing repeatedly within the 60 days, you’re ruining your chances of advancing in the appeals process.
Remember: claims that are denied in the initial level are usually denied in reconsideration, as well. Expect that you’ll have to go before a judge if you’re initial claim is denied.