I know this issue is present since at least 19w06a, but couldn't find any report about it.
You are unable to place blocks in certain locations adjacent to fences and walls. I have no information concerning the cause of this issue, it seems to be occuring randomly, although I might be wrong here.
It happened to me a few times, but I recorded only one and attached it below. Please note that the fact that the slabs disappear after a certain period of time is due to server lag, not the issue itself.
[media]Edit: I am able to place torches in the spots where I could not place slabs in the video
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Likely caused by invisible entities. Please attach (or provide a download link of) the world here so we can reproduce the issue.

OK, here is the download link: Download
The exact coordinates of the location in the video are -4482 71 908
Edit: The exact locations where you cannot place blocks seem to be changing from time to time. For example, today I was able to place blocks next to the other slabs in line seen at the beginning of the video, but was unable to place in the location of the cobble wall connecting two lines of walls on different heights (seen in the video as well) - after destroying it.
Can confirm with given world.
Seems to be a duplicate UUID entity. I went up to the area and ran "/kill @e[distance=..3,type=!player]
" and it killed an invisible cow that was in that block. Though that didn't seem to fully fix it, there still seemed to be another entity there that wasn't affected by the command. I had to use a piston and pushed the invisible entity out of the chunk. Once I did that, I left and rejoined the world, and the entity was gone. I hope that helps until Mojang fixes the issue that is causing this.

I'm having this problem on Single Player/Peaceful, trying to place a slab road. I tried flushing out invisible entities with water, but nothing is there. I also don't hear anything, like a chicken or a villager that could be standing there. I've got a strip of 3 blocks in a row where you can place under & 2 blocks over.
Download: https://ufile.io/lbx5l Screencap of the location included in the file. (BTW, NEKO's piston trick worked. After I ran a piston over all 3 blocks in a row, I was able to place the slabs on top).

I've just seen this in the latest snapshot 19w13b, the kill command and re-logging seem to partially fix the issue

This can happen with world saved in some of the snapshots released during February or early March. In more recent snapshots it should fix itself by either leaving the world and re-entering it or by teleporting away at least twice the view distance and then teleporting back.
If this issue still happens in the latest snapshot, with worlds saved in 1.13.x, please leave a note here.
If it happens with world saved in snapshots before 19w13a, do not comment on this issue unless the steps outlined above are not solving the issue.

Worlds with duplicated entities loaded in 1.14 Pre-Release 5 will have the entities deleted as long as the chunks that they're in are loaded one last time. The "Keeping entity" spam will appear in chat, but no more afterwards. Example