I have submitted a paper to Physical Review E some 15 months ago. The criticism of the two referees was deep and serious so they suggested a major revision. The editor agreed to publish the paper if I can correctly answer their questions and implement their suggestions. In order to do so, I had to perform calculations which turned out to be lengthy and elaborate, but I have finally finished them. Now I see that the status of the manuscript is 'not under active consideration'. Any idea about the meaning of that? Does it mean that the paper is finally rejected or can it be 'reactivated' by the editor? In the case of the former, can I move the manuscript to another publisher without further communication with the APS?
The APS system does not set a deadline for the authors to submit a revised manuscript. However, after a certain length of time (I believe it is about one year), a paper is automatically moved from "with authors" to the "not under active consideration" category. That is the same category used for papers that have been outright rejected, but categorical rejections from Physical Review journals are relatively rare. The letter your received, inviting you to resubmit if you feel you can overcome the referees' criticisms, is boilerplate, sent out in the response to every letter that the reviewers offer mild rejection recommendations for.
So you can resubmit the paper, although processing will probably be a bit slower than it might be otherwise. The editor will try to send the paper back the same referees, and they may not have have the clearest memories of your manuscript after all this time. They may not want to review it again at all, which will delay the whole process.