[CentOS] USB drive is "read-only file system" and cannot umount - how to fix

I 'just' noticed that at some point, my USB backup drive on my server is 
mounted as read-only and all of my background sync cron jobs have been 
failing.

So I need to fix this without rebooting the server.

I can VNC into the server and running "mount" shows:

/dev/sdc1 on /media/HD103SI type ext4 (rw,nosuid,nodev,uhelper=udisks)

and umount gets:

# umount /dev/sdc1
umount: /media/HD103SI: device is busy.
         (In some cases useful info about processes that use
          the device is found by lsof(8) or fuser(1))

How can I get this drive r/w?