This is not a fix, but I needed the space to give a sufficiently detailed explanation, please go easy on the down votes ;-)
I cannot give you any technical details on why this may happen, only to confirm that it does & you are not seeing anything truly unusual, though you do appear to be getting a very high initial fail-rate.
I've been doing a very similar task [playing adverts on in-store screens] for over 10 years now, with an install base of approx 2000 player/screens.
The workflow would appear to be the same - write once, read many.
In the early days, these were compact flash-based, which suffered very few card failures [though the screens themselves were a different story].
In the past 5 years, all have been SD-card based - with a phenomenal early fail-rate, giving precisely the symptoms you describe - jerky, halting video playback.
From our initial batch of SD cards we randomly selected a couple of hundred to send back to the factory in China. [I was not privy to that conversation so don't know the technical details] From that sample, it was estimated that approximately 15% had manufacturing defects sufficient to display slow read speeds after only a few thousand reads. The rest were deemed 'at spec'.
At worst, the failing cards will actually eventually crash the screens, requiring a power-cycle to recover. The 'bad but not terrible' cards will consistently give halting playback of varying severity, but not crash the players. If you watch the same video cycling on one of these, you will see the read halts are consistently at the same points in each cycle.
Empirically, they are not data-load dependant; it is just as likely to happen on a 10MB video as a 120MB video of the same length.
Our quick test on these, when we come to update the content seasonally, is just
'Format. If it works it goes back in the machine. If it fails it goes in the bin'
- very rough & ready but the customer will not pay to swap out cards unless they have totally failed.
The end 'result' is that after about 5 years, we are down to about 75% of the original card batch, all of which now just seem to keep working. Some still halt a little, but not enough to upset the customer.
My only, rather limp, conclusion is a pretty obvious "some keep going, some fail early"
Late note: If I were to start over at this task, I would use players that contain their own internal flash-based storage, to which you copy the video to be displayed just once, from a known-good SD card. We have a few hundred of these in use, & whilst the ones we have are horribly 'cheap & cheerful' the one thing they have in common is they don't suffer from playback fails.