Okay, mystery solved.
I had forgotten that I had included some links to other data table rows as extra columns in my Users data table.
It seems that, to my considerable surprise, the default behaviour is to download the whole content of those linked rows.
When it was reaching a row which was linked to a really large amount of data it was silently failing. When I tried to load that row directly in code it raised an error along the lines of “too much data to transfer” or something similar.
I’m still grumpy that in the context of fetching data table rows no error is shown and the process just stalls.