After a lot of trial and error I found out that the problem was not in the coding of the videos themselves, but in the memory limit of the server. My hosting provider changed the php version and with that the limits and this lead to the problem that larger videos would not display anymore - the loading script is simply aborted with "out of memory".
I did now adjust this limit and as far as I can see all videos load.
But due to the way I serve them, the complete video must download before it shows. Therefore you must wait a while until it's loaded.
For those technically interested:
All files of my galleries are saved outside of what is called the "document root". This means that a http command cannot access these files directly for example with "src=path/file.ext". I do this for security reasons, so that it is "impossible" to access these files via another way than through my gallery-site.
The disadvantage is that the files must be served by a script that reads the file and then passes it over to the displaying page. Although in the end the loading time is the same, the impression is slower, because a video title image is only shown when then complete video has been read and not, as usual, already when the first few frames are downloaded.
I am searching for better solutions, but until now I haven't found anything better. However, in the next days I'll put my time in editing images again to upload them for you!
Have a nice day!
Daniel