Thanks Berker. In this case the previous tests using the same NNTP connection object were skipped. First run:

test_unknown_command (test.test_nntplib.NetworkedNNTPTests) ... ok
test_welcome (test.test_nntplib.NetworkedNNTPTests) ... ok
test_with_statement (test.test_nntplib.NetworkedNNTPTests) ... skipped "Resource 'news.trigofacile.com' is not available"
test_xhdr (test.test_nntplib.NetworkedNNTPTests) ... skipped "Resource 'news.trigofacile.com' is not available"
test_xover (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_zlogin (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_zzquit (test.test_nntplib.NetworkedNNTPTests) ... ERROR

Subsequent retry:

test_xover (test.test_nntplib.NNTPv2Tests) ... ok
test_article_head_body (test.test_nntplib.NetworkedNNTPTests) ... skipped "Resource 'news.trigofacile.com' is not available"
test_capabilities (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_date (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_description (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_descriptions (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_group (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_help (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_list (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_list_active (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_newgroups (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_over (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_unknown_command (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_welcome (test.test_nntplib.NetworkedNNTPTests) ... ok
test_with_statement (test.test_nntplib.NetworkedNNTPTests) ... ok
test_xhdr (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_xover (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_zlogin (test.test_nntplib.NetworkedNNTPTests) ... ERROR
test_zzquit (test.test_nntplib.NetworkedNNTPTests) ... ERROR

Test_with_statement() is a special case because it starts a fresh NNTP connection, rather than reusing self.server. Test_welcome() is also different because it does not send any new commands to the server. But I presume the other tests all try to reuse the old timed-out self.server object. The skipped messages are evidence of this.

The easy solution which I mentioned above would be to change setUpClass() to setUp(), although this might slow the tests down a bit, reconnecting to the remote server for each test method.

The solution that I prefer would be as Antoine suggested, to run our own server. I think expanding the server I created in Issue 25859 with more commands would be good enough.