Q: What is the meaning of the status "Reject and Resubmit: Due on"?

The status of your manuscript clearly indicates the editorial decision: "Reject and resubmit." This means that the editor has seen some merit in your study, but it is not publishable in its current form. Usually, it would require extensive revision, in most cases, adding new experiments or redoing the data analysis. The revision that needs to be done is so extensive that it will require a lot of time. Therefore, the editor does not want to rush you by giving you a specific deadline for submitting the revised manuscript. That is why there is no clear deadline.

Usually, for a "Revise and resubmit," the status would also mention "Due on so-and-so date" which is a deadline for submitting your revised manuscript. But for a "Reject and resubmit," the editor also leaves the author free to submit the paper elsewhere in case he/she does not want to make the extensive changes that are usually required.  It is definitely an encouragement to resubmit, and it is clear that the editor likes the topic of your paper and is willing to give it another chance. 

Related reading: 

• Does my rejection letter suggest that I will get a second chance?
• Should I revise my paper and submit it to the same journal?
• Will my paper be accepted if I make the revisions suggested?