First you need to know how these two types are distinguished. Microsoft has some documentation here: http://www.microsoft.com/whdc/archive/usbfaq.mspx
The removable media device setting is a flag contained within the SCSI Inquiry Data response to the SCSI Inquiry command. Bit 7 of byte 1 (indexed from 0) is the Removable Media Bit (RMB). An RMB set to zero indicates that the device is not a removable media device. An RMB of one indicates that the device is a removable media device. Drivers obtain this information by using the StorageDeviceProperty request.
So you need to change that bit. One way would be to change the firmware in the disk's controller using a vendor specific tool, but this is not always possible. Assuming you use an USB drive, you might want to do a search on the USB vendor/device ID to see if there is a possibility to change that bit.
The other (OS specific) way would be to use a filter driver. Since one usually wants to convert removable to fixed disks (since there are limitations for removable drives on Windows) there are filters available e.g. dummydisk.sys by Anton Bassov but I don't know of a driver that does the conversion in the opposite direction. It might be possible to edit the drivers's code to accomplish this but I haven't looked into this.
Since there is probably no universal solution that always works you might just want to use another tool that does not have this dumb limitation to backup your data.
Thanks for the answer:) I tried searching for software that converts fixed disks to removable drives, but in vain. – Ashwin – 2012-07-08T04:19:57.523