The Everything icon disappearing from the system tray or notification area can occur if Everything crashes.
Usually this is a crash with stack corruption and no error message is shown.
Please make sure you have the latest version of Everything and enable shell max path:
In Everything, type in the following search and press ENTER:
/shell_max_path=1
If successful, you should see shell_max_path=1 in the status bar for a few seconds.
Close the Everything window to ensure settings are saved to disk.