There is a slight issue with the Divi Theme when you try to put a lot of links in the header bar, which sees the links shift down a row and the search box magnifying glass icon to get pushed down the page. Here's how to fix it.
First, a look at the issue. Here is how the header looks if you add a lot of links into the header menu:
I've marked the position of the search icon in orange. Note also that the links have slipped down a row.
The problem here is that the area assigned to the links is allowed to be as wide as the header itself (1080px in fullscreen mode and 960px when the screen is shrunk). So if there are enough links the area becomes too wide to sit on one line with the other components and is forced to move onto its own line below the logo. And there is no room on this new row for the magnifying glass so it is moved down another row still. Combine that with the fact that the links themselves take up two rows and we see the whole thing is now taking up 4 rows.
Here is the result of implementing the fix:
Fixing the Search Icon Issue using Divi Booster
Divi > Divi Booster > Header > Main Header > Fix header menu width / magnifying glass issue
Simply enable the option, save, and the icon should be restored to its correct position.
Fixing the Search Icon Issue using CSS
The following CSS can be used to restore the search icon to its original position in the header:
Related Post: Adding CSS to the Divi Theme
Fixing the Search Icon Issue using CSS / JS (Old Method)
I used to recommend the following fix, though it's a bit more complex than the above and no longer works in recent versions of Divi. I've left it here in case you find yourself using an old version of Divi and unable to get the other options to work.
We can fix the issue by setting a maximum width on the element containing the links which is about 100px plus the width of the logo shorter than the width of the header itself.
Technical note: I'm using get(0).width in the jQuery instead of .width directly, so that the fix will work even if the header is initially hidden.