More than once I’ve had this happen. For one reason or another, a change to the SharePoint Search Topology needed to be made.
Go in, add a new crawler or partition index, click save, and the page gets stuck on
Please wait while your changes are processed for SharePoint Server Search.
Okay, one thing I’ve found to help avoid this issue. Make sure the SharePoint Admin service is running on each box in the farm BEFORE making any updates to the search topo.
Navigate to timer job definitions.
Change the View to Service
Service: SharePoint Server Search
Run the Configuring the existing search service application SharePoint Server Search job.
Go back and check the modify topology page.
Remember, make sure the Admin Service is running!
In the comments, user SM pointed out that the Configuring the existing search…. job may not appear unless it needs to be executed.