Showing of Registered menu item is inconsistent

[Lxg]

I have recently found that the one menu group which is available only to registered users when signed on is somewhat inconsistent in its display. We have only the one menu group - called 'for members' which is hidden from public viewers. Two members have reported that when they sign in they do not see the 'For members' menu. However, if they change to any other (public) menu except the home page, then 'For members' displays. If they switch to the home page, the 'For members' disappears again. I have asked them to clear cache - no change. They have tried on windows 10 with Chrome and FF and on the Android browser and Firefox on a tablet, on Safari on an iPad and Firefox on Windows 10. I do not have the same problem either with my administrator sign-on or with another signon that is defined the same as theirs. I have tried with Windows 10 - FF, Chrome and Edge and on Linux FF- no problem. The one thing I can think of that might be linked to their problem is that using extension sslredirect I have ssl on the homepage where the login button is found but not on others.
Unfortunately, I am not certain when this showed up. I am finding that my club members are not reporting such problems when they find it so it may have been here for some time.
I don't know where to look to find this problem, especially since I don't seem to have the problem.

Joomla! Instance :: Joomla! 3.7.2-Stable (Amani) 22-May-2017
Joomla! Configured :: Yes | Read-Only (444) | Owner: --protected-- . (uid: /gid: ) | Group: --protected-- (gid: ) | Valid For: 3.7
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Host Configuration :: OS: Linux | OS Version: 2.6.32-673.26.1.lve1.4.25.el6.x86_64 | Technology: x86_64 | Web Server: Apache | Encoding: gzip, deflate | Doc Root: /home/ottawaoc/public_html | System TMP Writable: Yes

PHP Configuration :: Version: 7.1.4 | PHP API: cgi-fcgi | Session Path Writable: No | Display Errors: | Error Reporting: 22527 | Log Errors To: | Last Known Error: | Register Globals: | Magic Quotes: | Safe Mode: | Open Base: | Uploads: 1 | Max. Upload Size: 16 M | Max. POST Size: 8M | Max. Input Time: 60 | Max. Execution Time: 30 | Memory Limit: 128M

MySQL Configuration :: Version: 5.5.55-cll (Client:5.5.55) | Host: --protected-- (--protected--) | Collation: latin1_swedish_ci (Character Set: latin1) | Database Size: 60.23 MiB | #of Tables: 135

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Potential Missing Extensions :: mysql | suhosin |

Switch User Environment (Experimental) :: PHP CGI: Yes | Server SU: Yes | PHP SU: Yes | Custom SU (LiteSpeed/Cloud/Grid): No
Potential Ownership Issues: Maybe

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Elevated Permissions (First 10) ::

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