A bug exists in the Search widget such that when the sources menu is open, and you click the arrow button on the left of the widget (presumably to close it), the menu will close, and then immediately re-open. This can be verified in the sample "Search widget with multiple sources". This behavior has also been present in releases prior to 4.22, but the suggested fix below may not work in anything other than 4.22.
If you have a locally hosted copy of the API, you can fix this problem by doing the following find-and-replace in esri/widgets/Search.js:
Search for:
onfocus:this._clearActiveMenu,afterCreate:G.storeNode,
Replace with:
onfocus:function(){if(this.activeMenu!="source")this._clearActiveMenu();}.bind(this),afterCreate:G.storeNode,