In certain countries, such as South Africa, a patent which has lapsed unintentionally may be restored if there has been no undue delay in bringing the application for restoration, and it can be shown that the lapsing was unintentional, and there is a good reason to restore the patent and it is valuable to the patentee. http://www.cipc.co.za/index.php/faqs/patents/
It is not considered a good reason that the patentee could not afford to pay the renewal fee or just forgot, and a patentee of a lapsed patent would need to show evidence of not being aware of the need for the renewal e.g. a renewal notification from their patent attorney being lost in the mail, ill health at the time of the renewal fee falling due, confusion during the transfer of a patent from one patentee to another, or the like. The application for restoration must be accompanied by an Affidavit explaining the failure to pay the renewal fee, the lack of delay, and requesting restoration of the patent.
In the example of South Africa, if the Registrar of Patents is satisfied that the omission was unintentional and that no undue delay has occurred in the making of the application, he shall advertise the application in the prescribed manner, and any objector may within two months of the publication, give notice of opposition to the restoration of the patent. If there is no opposition, the Registrar shall restore the patent and then the arrear renewal fees must be paid and the patent will once again be in force and future renewal fees will once again be payable. If there is opposition to the application for Restoration then the application will be heard in the Court of the Commissioner of Patents who, after considering the evidence and legal arguments as in any Court Application, will decide the matter and either restore the patent or dismiss the application for restoration.