"doth" system test fails intermittently with "The single DIG instance has stopped prematurely"

Sample failure: https://gitlab.isc.org/isc-private/bind9/-/jobs/2819987

I:doth:checking server quotas for both encrypted and unencrypted HTTP (170)
Traceback (most recent call last):
  File "/builds/isc-private/bind9/bin/tests/system/doth/stress_http_quota.py", line 252, in <module>
    sys.exit(main())
  File "/builds/isc-private/bind9/bin/tests/system/doth/stress_http_quota.py", line 244, in main
    run_test(http_secure=True)
  File "/builds/isc-private/bind9/bin/tests/system/doth/stress_http_quota.py", line 225, in run_test
    assert (
AssertionError: The single DIG instance has stopped prematurely
I:doth:failed

Just in the public BIND 9 project in the past 6 days, this failure mode has been triggered over 50 times.

Except for two outliers, it always happened in system test jobs with either ASAN or TSAN enabled and, AFAICT, only for MRs targeting the main branch, so this might be related to !6040 (merged) (see also #3595 (closed)).