One possible culprit would be an extension. You can view, disable, and often remove unwanted or unknown extensions on the Add-ons page. Either:

• Command+Shift+a (Windows: Ctrl+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then cast a critical eye over the list on the right side. All extensions are optional. If in doubt, disable. If you find something called Searchme, remove that for sure.

Often a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Any improvement in Firefox's memory?

This article lists some other steps to investigate this kind of problem: How to fix preferences that won't save.

Type about:addons<enter> in the address bar to open your Add-ons Manager. Hot key; <Control>(Mac=<Command>)<Shift> A)

In the Add-ons Manager, on the left, select Extensions. Remove Yahoo Anything. Now do the same in the computers Programs Folder.

Windows: Start > Control Panel > Uninstall Programs. Mac: Open the "Applications" folder. Linux: Check your user manual.

https://support.mozilla.org/en-US/kb/how-to-fix-preferences-wont-save

Note: Some software, like Advanced SystemCare with Surfing Protection, can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.