Can't mount devpts on /newroot/dev/pts: Too many open files

Hi,
I'm using bubblewrap to run several hundreds of thousands of untrusted programming contest submissions.
However, after some time I get `Can't mount devpts on /newroot/dev/pts: Too many open files`, and sometimes `bwrap: Can't mount proc on /newroot/proc: Too many open files`.
Strangely, after restarting the process, the error appears much sooner (after a few hundreds of bwrap invocations).
I tried to increase the corresponding operating system limit but that does not seem to be the problem.
Does anybody have an idea what the problem might be?