Stats button disappears momentarily when typing in the search bar

Created by: rvantonder

Chrome browser. Reproduced on Mac and Windows

https://user-images.githubusercontent.com/888624/111533410-f93c0f00-8723-11eb-81d4-0390497de841.mp4

CC @sourcegraph/frontend-platform @sourcegraph/search, don't know who the right team is for this.