2015/2/23にApp StoreからPhotoshop Elements 12 Editorを購入し、先日まで、使用していたが、突然開けなくなった！どうしたら良いか？

Mac only PSE problem https://www.macnn.com/articles/15/11/12/apple.has.issued.new.certificate.that.expires.in.2035.131249/

http://www.macworld.com/article/3004917/security/mas-extinction-apple-letting-a-certificate-die-isnt-a-security-issue-just-an-embarrassment.html

PSE 10, 11, 12, 13, 14 - https://helpx.adobe.com/photoshop-elements/kb/photoshop-elements-downloads.html

You can also download the trial version of the software thru the page linked below and then use your current serial number to activate it.  Be sure to follow the steps outlined in the Note: Very Important Instructions section on the download pages at this site and have cookies enabled in your browser or else the download will not work properly.
                               
Photoshop/Premiere Elements 12: http://prodesigntools.com/photoshop-elements-12-direct-download-links-premiere.html