Even though I cannot reproduce this issue, please do not close it as incomplete. Because I know it is incomplete, I tried e-mailing it to support, and they told me to take it here.
Even though these aren't reliable reproduction steps, it is information about the conditions under which the issue happened. It is my hope that people can pool their knowledge and experiences and we can find out more. Failing that, the developers know the source code and may very well have a theory as to the cause anyway.
Here is the story:
• I made a portal and went to the Nether and back a few times. No problem.
• I built a cobblestone room around the portal on the Nether side using bottom-half slabs for the floor and ceiling. Also adjacent to the portal was a door leading to some stairs heading downward to a rear entrance/exit.
• Upon returning to the Overworld, I exited through a second portal that had been spontaneously created (the one on the left). No matter which portal was used to get to the Nether, this portal was always the exit portal going forward.
• Many days go by. A creeper manages to get through a portal to the Nether and blows up six slabs in front of the portal on the Nether side.
• The next time I portal to the Nether, I exit through another spontaneously generated portal: The one on the roof.
• Now, even after repairing the floor, the one on the roof is the only portal that brings me to the Nether. My two original portals are completely nonfunctional as exit portals.
Also note that the portals can be mined and abused for infinite obsidian.
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I had something vaguely similar on one of my maps on 0.13, where I moved the portal, but would still respawn in the place where the original stood (but didn't regenerate), even though it meant that I spawned into dirt blocks and suffocated.

Though it's unlikely to be a duplicate it relates to MCPE-14076.
Also note that the portals can be mined and abused for infinite obsidian.
FYI that's an intended property of nether portals. Even without the bug you can still mine and regenerate portals to farm obsidian.

Adding 0.15.0 Beta build 1 to the Affected Versions per MCPE-14934.

Please respond and add the current version if you can reproduce this issue.

Affects 0.16.2.
Are you able to upload a copy of the world save?

Not exactly. The original save the screenshots are from is lost. Last night it happened in another world, but my son mined the extra portal and it did not regenerate. I will upload it anyway, however. If QA makes a new world with the same seed and duplicates the conditions, including building what my son built on the nether side (doing this and traveling back to the overworld is what triggers the portal duplication), it should reproduce.
EDIT: correction, the file is 36 MB zipped, well over the 10 MB limit for attachments. Here is a Dropbox link: https://www.dropbox.com/s/awkvecqvssue1uk/wyoCAJC1AgA%3D.zip?dl=0

I can also confirm this was a problem. When a portal was damaged, say by a ghast, it would create new portal in overworld after being repaired, and after that things got messy, travel thru the portal seemed to create new exit portals at the same location in both directions. This behavior disapeared in 1.0 and replaced by the arguably worse behavior noted in MCPE-19696

This appears to be fixed in 1.0.

This problem still exists in version 1.10.1.
I created a potal and went into Nether. When I returned a few seconds later, I appeared in another portal which automatically formed in a cave 100 blocks away from the first portal.
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This has also happened to me on three separate occasions now. First about the same height one hu dred blocks away floating above the ocean. Destroyed that one to fix the issue because it was taking priority. Second it reappeared about the same location as the original dupe only this time at BEDROCK, IN A MINESHAFT IN FRONT OF A SPIDER SPAWNER. It was a bit surprising when I had expected to be at my original built on top of home sweet home... had to live there for a minute and dig my way to the surface. Third just occurred which frustrated me to taking a break. Placed a new nether portal on top of a peak that dropped me into lava with all my faithful gear... a long fall. Always crouch and peek I learned the hard way. Then it duped when I returned after going back to explore gearless, level less and sad. Duped to another peak about 200 blocks away... now I'm taking a break.
Will post pics if needed.