Start by making sure the drive is not excluded from being indexed by opening System Preferences > Spotlight > Privacy.
The subsequent list you should see on this page is a list of all locations that Spotlight is prohibited from searching. If your drive is listed, select it and remove it from the list.
If your drive was listed and you removed it from this list then your problem will be resolved the next time Spotlight re-indexes your files.
You can force Spotlight to re-index your files and if your drive was not on the previous list then this would be the next step in attempting to resolve the issue. Open Terminal.app and issue the following command to clear out Any existing index and have Spotlight do a completely fresh re-index of your entire system.
sudo mdutil -Ea
mdutil -ai off
mdutil -ai on
Alternatively if you want to just re-index the drive in question you can have Spotlight re-index any specific location by modifying the command slightly like so
sudo mdutil -E /Volumes/YourDriveName
If the issue is still not resolved open Disk Utility and run First Aid on the drive to ensure there are no errors. Also be sure that if you disconnect the drive you are unmounting it properly before physically disconnecting it and you are not disconnecting it while the index is in progress.