It is possible for certain software programs to interfere in optical drive operation, including Daemon Tools and Alcohol 120. Certain malware/virus infections can also cause some problems in burning, but don't cause drivers to go missing as far as I am aware. Internet security settings interfering with drivers on an optical drive would be a new one for me.
Since this is an IDE interface drive, you might try deleting the IDE controller channel that this drive is on. You can find this in Device Manager. Don't delete the channel if your hard drive with your operating system is on this same channel. I don't know if your optical drive is on the Primary or Secondary channel.
Once deleted, reboot and let the operating system find the "new" hardware. Drivers should be reinstalled by Windows.
Optical drives have the drivers within all modern operating systems.