When I play back a MIDI region, often some notes end up not being played. This happens consistently enough that phrases longer than a couple of bars become near impossible to play back correctly even with multiple tries.
Is this a known issue? Is there a fix/workaround?
Please remember that you can make the gap as short as 1 sample and the problem will vanish. Just to clarify, nobody can hear a 1 sample gap 
I’ve had the problem with notes in the middle of region as well, when they are preceded by a note that ends exactly when the other one starts. For example, if I lay down 8 notes side-by-side occupying a whole bar, some of them will not play. The workaround is shortening the preceding note so that there’s a small gap between them.
I did try that workaround (with note at beginning of region), and I find it to work most of the time. Notes do however skip in the middle of the region as well, although the issue seems to have gone away for the time being, for whatever reason.
The known bug is that notes that coincide exactly with region or loop or range boundaries will sometimes not be played. I am not so aware of issues with notes in the middle of a region.
We are working hard to fix this (fundamental) issue in Ardour 6.
The workaround for the first problem is to slightly extend the region edges or slightly shrink the note onsets/ends (turn the grid off and move them by tiny amounts.