Using the per-revision bisect providing the bisect results,

Good build : 54.0.2832.0 (412743)
Bad build : 54.0.2833.0 (413134)

You are probably looking for a change made after 420549 (known good), but no later than 420550 (first known bad).
CHANGELOG URL:
  https://chromium.googlesource.com/chromium/src/+log/697e6fc2d3a21124b983953086d525576fdf15f5..cd81492dada5b5ad4c2f6914323145cd8a541eb2

Note: Adding RB Label as this is a recent Regression. Please remove if not required.
@ tommycli -- Could you please look into the issue.

actually, the repro steps are even simpler.

0. navigate to chrome://md-settings
1. click Advanced toggle
2. open side nav

what do you expect?
no change to the visibility of showing the advanced section

what happens instead?
the advanced section hides when you open the side nav.

so there's a few issues here:

1) all this tracking of whether advanced stuff is showing is complex

fix: https://codereview.chromium.org/2420833002/

2) when you use data binding for <paper-submenu opened="{{thing}}"> it doesn't work well (if you start with a truthy value the submenu takes a few clicks to right itself)

chrome-side: https://codereview.chromium.org/2412343004
upstream: https://github.com/PolymerElements/paper-menu/pull/107

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/5f9bf9e2c68a25b9bd02639c70d31c9c627cb458

commit 5f9bf9e2c68a25b9bd02639c70d31c9c627cb458
Author: dbeam <dbeam@chromium.org>
Date: Mon Oct 17 22:35:02 2016

MD Settings: rework how advanced UI shows

Before, there were some events.  And booleans.  And maybe some binding.
It generally worked, but it was a little complex.  Now there's just
2-way bindings everywhere.  Changes from toggling the advanced buttons
in the main UI or in the nav flow to all other parties.  I also checked
that opening a page like /clearBrowserData works (all advanced toggles
and states work as expected).

Also, we probably had to call .open() or .close() explicitly because
<paper-submenu> has a bug when using only the opened="{{binding}}":
https://github.com/PolymerElements/paper-menu/issues/88

A fix for that bug is here:
https://github.com/PolymerElements/paper-menu/pull/107

I might also make a local change in Chrome's fork of Polymer if we must.

R=dpapad@chromium.org
BUG= 650951 
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:closure_compilation

Review-Url: https://codereview.chromium.org/2420833002
Cr-Commit-Position: refs/heads/master@{#425795}

[modify] https://crrev.com/5f9bf9e2c68a25b9bd02639c70d31c9c627cb458/chrome/browser/resources/settings/settings_main/settings_main.html
[modify] https://crrev.com/5f9bf9e2c68a25b9bd02639c70d31c9c627cb458/chrome/browser/resources/settings/settings_main/settings_main.js
[modify] https://crrev.com/5f9bf9e2c68a25b9bd02639c70d31c9c627cb458/chrome/browser/resources/settings/settings_menu/settings_menu.html
[modify] https://crrev.com/5f9bf9e2c68a25b9bd02639c70d31c9c627cb458/chrome/browser/resources/settings/settings_menu/settings_menu.js
[modify] https://crrev.com/5f9bf9e2c68a25b9bd02639c70d31c9c627cb458/chrome/browser/resources/settings/settings_ui/settings_ui.html
[modify] https://crrev.com/5f9bf9e2c68a25b9bd02639c70d31c9c627cb458/chrome/browser/resources/settings/settings_ui/settings_ui.js
[modify] https://crrev.com/5f9bf9e2c68a25b9bd02639c70d31c9c627cb458/chrome/test/data/webui/settings/settings_menu_test.js

https://codereview.chromium.org/2427743003 will address the double-tap issue without a Polymer change (but i'll still be tracking the Github PR)

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/bb372ed35e94c5b140a09a3190cb4cfd058e6522

commit bb372ed35e94c5b140a09a3190cb4cfd058e6522
Author: dbeam <dbeam@chromium.org>
Date: Tue Oct 18 02:06:05 2016

MD Settings: fix double-tap to hide advanced bug

R=dpapad@chromium.org
BUG= 650951 
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:closure_compilation

Review-Url: https://codereview.chromium.org/2427743003
Cr-Commit-Position: refs/heads/master@{#425856}

[modify] https://crrev.com/bb372ed35e94c5b140a09a3190cb4cfd058e6522/chrome/browser/resources/settings/settings_menu/settings_menu.js
[modify] https://crrev.com/bb372ed35e94c5b140a09a3190cb4cfd058e6522/chrome/test/data/webui/settings/settings_ui_browsertest.js

Verified on ChromeOS 8920.0.0, 56.0.2897.0