If one of the servers in your Search Application Topology is showing a Status of Not Responding, try and restart service app for the server in question.

One of my Crawl Components was not responding, but the server was online and working.  The script below helped to re-sync the server.

-identity “Search Service Application”

Replace Search Service Application with the name of your Search App.

$SearchApp = Get-SPEnterpriseSearchServiceApplication -identity "Search Service Application"

$SearchApp | Get-SPEnterpriseSearchQueryTopology | Get-SPEnterpriseSearchQueryComponent | Where-Object {$_.ServerName -eq 'Server Name That is Stuck'}  | Restart-SPEnterpriseSearchQueryComponent