I've tried to reproduce the failure but every time I run it against a daisy in the lab, the test passes :-/

I did notice that the update_engine.log is empty during each of failures. 
So my first guess is that calling update_engine_client --update right after calling restart update-engine means the update request is missed

However, on a couple of occasions when I ran it from my desk, even though the test passed the update_engine.log was still empty (empty meaning it just had the first few startup entries, no update requests) 

So I am thinking that sometimes when we sign out of chrome (as this test does) update_engine restarts/terminates and the log we collect afterwards is a not the one from the test.

Looking at it again. Daisy is failing before we even sign into Chrome. I'll grab somemore update_engine logs anyway because I think we are not saving the one from the test on daisy.  

Sign in failed could be of this https://crbug.com/833563 ?

The following revision refers to this bug:
  https://chromium.googlesource.com/chromiumos/third_party/autotest/+/711ede943a5939faa609cb621b6e5915ccdd568d

commit 711ede943a5939faa609cb621b6e5915ccdd568d
Author: David Haddock <dhaddock@chromium.org>
Date: Tue Apr 17 22:53:11 2018

Collect more logs to figure out why EOL is failing on daisy.

This CL makes this test inherit from the base class for update engine
tests and grabs more update engine logs.

BUG= chromium:833518 
TEST=autoupdate_EOL

Change-Id: Ia6354acb6d2e3c63be8c343151bd2e239fa0499e
Reviewed-on: https://chromium-review.googlesource.com/1014473
Commit-Ready: David Haddock <dhaddock@chromium.org>
Tested-by: David Haddock <dhaddock@chromium.org>
Reviewed-by: Katherine Threlkeld <kathrelkeld@chromium.org>

[modify] https://crrev.com/711ede943a5939faa609cb621b6e5915ccdd568d/client/cros/update_engine/update_engine_test.py
[modify] https://crrev.com/711ede943a5939faa609cb621b6e5915ccdd568d/client/site_tests/autoupdate_EOL/autoupdate_EOL.py

The following revision refers to this bug:
  https://chromium.googlesource.com/chromiumos/third_party/autotest/+/2fd9aec66ebf1411565262dea77f7599db17fe4f

commit 2fd9aec66ebf1411565262dea77f7599db17fe4f
Author: David Haddock <dhaddock@chromium.org>
Date: Thu Apr 26 06:00:32 2018

More refactoring and fixes for some failing tests.

Refactoring includes:
- Added Functions for getting multiple logs.
- Remove setting self._host in every test
- Remove printing update URL in every test.

Fixes:
EOL: Daisy is failing because we are calling update too soon after
restarting update engine. So I will just not restart it before the test.

P2P: I am resetting the current url index before I reboot.

Disconnect internet: Occasionally it fails because the progress moves
from 0.200001 to 0.200002. So I am just waiting for a bit for it to
settle.

Cellular tests: Have been failing after I incorrectly changed a variable
name from cellular to public.

BUG= chromium:833518 
BUG= chromium:817913 
BUG= chromium:817908 
TEST=all au tests.

Change-Id: I208b54e6c7c4076f4a6ecadb94e4c1bac69a3be7
Reviewed-on: https://chromium-review.googlesource.com/1025398
Commit-Ready: David Haddock <dhaddock@chromium.org>
Tested-by: David Haddock <dhaddock@chromium.org>
Reviewed-by: Amin Hassani <ahassani@chromium.org>

[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/client/cros/update_engine/update_engine_util.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/client/site_tests/autoupdate_EOL/autoupdate_EOL.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/server/site_tests/autoupdate_NonBlockingOOBEUpdate/autoupdate_NonBlockingOOBEUpdate.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/server/site_tests/autoupdate_OmahaResponse/autoupdate_OmahaResponse.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/server/site_tests/autoupdate_P2P/autoupdate_P2P.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/client/site_tests/autoupdate_Backoff/autoupdate_Backoff.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/client/site_tests/autoupdate_DisconnectReconnectNetwork/autoupdate_DisconnectReconnectNetwork.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/client/site_tests/autoupdate_StartOOBEUpdate/autoupdate_StartOOBEUpdate.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/client/cros/update_engine/nano_omaha_devserver.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/server/site_tests/autoupdate_Cellular/autoupdate_Cellular.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/client/cros/update_engine/update_engine_test.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/server/cros/update_engine/update_engine_test.py
[modify] https://crrev.com/2fd9aec66ebf1411565262dea77f7599db17fe4f/server/site_tests/autoupdate_ForcedOOBEUpdate/autoupdate_ForcedOOBEUpdate.py

Latest changes fixed this issue:
https://stainless.corp.google.com/search?test=%5Eautoupdate%5C_EOL%24&exclude_non_release=true&exclude_cts=true&col=build&row=board_model&view=matrix&first_date=2018-04-25&last_date=2018-05-01