Usually, you can stop the startup disk from spinning down by going to System Preferences > Energy Saver, then unchecking "Put the hard disks to sleep when possible". However, whilst this is certainly true for the startup disk, whether this is adhered to by external drives seems to be wholly dependant on the drive itself.
This page has more information, including a description of your problem, but also says
Second, some non-startup drives simply ignore the setting of Put the hard disk(s) to sleep when possible and spin down on their own schedule. This appears to be a function of either the drive itself or, in the case of external drives, the firmware or chipset employed in the drive's enclosure. In such a case the drive's Standby behavior cannot be changed. One can contact the manufacturer of the drive or enclosure to see if a firmware update is available to improve its cooperation with Mac OS X power management.
The only other way I can think of around this, if the above doesn't work, is forcibly keeping the drive awake. To do this you could simply set up a script to
touch a file on the external drive at fixed intervals.