Simpletest fatal error without message locally my unit tests run just fine. On my online dev server, they fail and I don't get any error message despite "The test did not complete due to a fatal error." in the test messages and "An internal server error occurred. Please try again later." as return text of the batch process. No entry in the default error log, no error log file in the temporary simpletest public directory.

Is there any way to debug this and get the stack trace etc?

When I run the tests via Drush, they work just fine. This issue occurs only with the testing user interface and might be related to the PHP memory_limit as I run on a shared host.

The point where the test fails seems to be arbitrary: Sometimes it comes as far as 200 asserts before failing, sometimes the fatal error occurs after only 40 assertions. Also the test function from which the error is thrown differs, but they all belong to the same class.
Figured it out ... The hoster I use (uberspace.de) has a timeout for script execution time. Some Simpletest tests do not respond for several minutes, which triggered the timeout.