If you get the 'An Import is already in progress' message on the feed list screen and it doesn't disappear after a few hours then the current import has probably failed.
In the short term, delete the file 'admin/datafiles/import.lck' to get rid of the message. This enables you to run the import again.
If you keep getting this message check the log files. If you are doing an 'Import ALL' this is stored in 'admin/logs/all.txt' - note that this might be quite large!
If the bottom of the log file always shows the process stopping in the same place then it could be a problem with the particular feed it is consistently processing at that point. Try temporarily deleting that feed to see if the import then finishes.
If the process seems to stop in different positions each time then this usually indicates that you are hitting a resource limit / timeout on your host, e.g. some hosts limit the number of MySQL operations you can perform per hour, and as the import process is a database intensive operation you may be triggering that (this is especially common on shared hosting and might indicate that you need to upgrade your hosting package, e.g. to VPS level).
From user feedback < 500k products should work fine on most shared hosting packages. 500k to 2m should be fine on VPS level hosting. Above 2m products you might want to start thinking about dedicated hosting.