If you are denied on your Social Security Disability or SSI benefit claim, you should request an appeal immediately, within the 60-day deadline. In some cases, you should do this yourself personally even if you have legalrepresentation, simply to have the appeal request "officially" on record as soon as possible.
Amazingly, most disability claims that are denied are not appealed. Claimants either give up on the process, or file a appeal too late, or file a brand new claim (a mistake). A failure to appeal timely or filing a brand new claim will have the same end result: a loss of appeal rights and having to start over at the very beginning with a new Social Security Disability or SSI application.
It is during the Social Security disability appeals process (as opposed to making a new application) that a claimant has the best chance of winning a claim and being awarded benefits. Filing a new application, either because someone thought it was a good idea or missed the appeal deadline, is simply a waste of valuable time. Subsequent applications for disability will likely be denied for the same reasons as the first application. In either case, missing an appeal deadline, or starting a new application instead of appealing a denial, are situations to be avoided because they waste a significant amount of time. (If you did miss your appeal deadeline, and don't have a good reason, you should reapply for disability.)