I'm assuming you were trying to Join the Polylines with the curved segments and not the straight line segments that meet in the center or the Rectangle that surrounds everything else. My experiments did not cause Joined pieces to disappear, but that's not the first time my system has had different results than other people.
I have noticed, however, that the curved piece in the lower right does not intersect with any other Polylines at either end (shoots past on the center right, undershoots on the center bottom). Disconnects for the lower left Polyline, too.
The Polyline at the upper left connects to the Rectangle at the top center, but not the vertex of the Polyline at the upper right.
So... you will have to fix these before trying to Join them.
You can prevent your originals from disappearing if you disable the Delete Original Objects icon in the Inspector Bar while the Join Polylines function is active, but I really doubt that is the problem. However, you would have to have more than 1 layer for my supposition to be the case.
TC Pro Platinum 2018, 2017, 2016 & 2015 (all with LightWorks & RedSDK) & V21
System: i7-5820K @ 3.30GHz, ASRock X99 Extreme4, 16GB DDR4-2133 RAM, Gigabyte GTX 970, Samsung NVMe SSD 950 (256GB), Windows 7 Pro (64-bit) SP1