If you discover that the search service application in your environment is paused (look under “administrative status” under Search Administration in Central Administration), you can first try to find the reason, and if the service is stuck, you can try to force it to resume. Typically, the administrative status could be “Paused for:External request”. If you have this issue, start SharePoint 2013 Management Shell and do the following
Get the search service application
$ssa = Get-SPEnterpriseSearchServiceApplication “Search Service Application”
Check if the SSA is paused (return “True” if paused)
$ssa.IsPaused() -ne 0
To check for the reason, run one of the commands described on the following TechNet article:
https://technet.microsoft.com/en-us/library/dn745901(v=office.15).aspx
Example: “($ssa.IsPaused() -band 0x04) -ne 0“: “A backup of the Volume Shadow Copy Service (VSS) is in progress”
If you did not find a reason using the above commands, or if it is not a “logical” reason, try to force the SSA to resume:
$ssa.ForceResume($ssa.IsPaused())
If this does not help, you might have to delete the indexes, here is an article about how to do that:
http://blogs.msdn.com/b/kristopherloranger/archive/2014/09/26/sharepoint-2013-on-prem-reset-index-stuck-resolution.aspx
umeaworks 
Great article! In my scenario the SSA was stuck in “Paused for external request, paused for reindex”. I also had an orhan content processing Component in the search topology. I tried $ssa.resume() and $ssa.ForceResume(), but could not get the SSA running again. I ended up backing up the search administration database, then deleting the SSA, then restoring the search admin database and then I used powershell to create a new SSA with parameters to use the restored admin database. In that way I could keep the managed properties we had added.
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Great article, helped me to resolve my issue.
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