"An administrative law judge (ALJ) has the authority to reopen an initial, revised or reconsidered determination, or a hearing decision or revised hearing decision under title II or title XVI of the Social Security Act for any reason within 12 months from the date of the notice of the initial determination (see 20 CFR 404.988(a) and 416.1488(a))."
In order to get a prior application reopened, so that you can obtain all of you back benefits, you need to ask the ALJ to reopen it at your hearing. Additionally, you typically need a reason to request reopening. It could be a simple reason, such as you missed the deadline to appeal because you were in the hospital or did not receive your mail because you moved. You may have mental illness that prevented you from understanding your rights or you may have been trying to gather all of your medical records before submitting your appeal. As long as you have a reason, the ALJ must consider a reopening request that is within a 12 month period from the date of the notice of the initial determination. The ALJ is not automatically required to reopen a previous determination, even if it is within 12 months, but the ALJ cannot automatically deny a request to reopen a prior application. If the ALJ reopens a prior application, it should result in you receiving a larger back benefit amount or, in other words, all of the benefits you are entitled to since you filed your first application.