Are you using Internet Explorer? If so, you probably have Compatibility Mode enabled. A couple things, try a different browser and it will most likely reappear. If you are on IE, try removing the site from the list and/or uncheck Display Intranet sites in compatibility mode.
Thanks for your speedy response.
I have proposed this to our key stakeholders to approve trying this.
I believe the issue you have seen here was known Problem 5924: Web Access incorrectly detects IE 8/9/10/11 in Compatibility Mode as IE7
Note: When IE is configured to use Compatibility View for local intranet sites the browser is incorrectly detected by Web Access as IE7 which then limits access to only Self Service, thus removing the switch icon
This problem was identified in the release of 7.7.1 and was fixed in the release of 7.7.3, I would therefore personally recommend to upgrade to the latest version of 7.8.2
If you cant upgrade in the short term, another browser could be used to access Web Access or if IE is business browser of choice, then you could apply the below workaround.
-- Add the Web Access site to the internet zone this will mean it is not picked up by the intranet zone (This may need to be applied via GPO)
Hope this helps