It sounds like the drive is locked during the burn and not being released.
DLA - a common packet writing software program from Sonic is notorious for
doing this. Are you trying to open the drive using the eject button or are
you right clicking and using the "eject" option in the context menu? You
should try using the soft eject from the context menu rather than the button
on the device. Depending on the software you are using to burn with i.e.
packet writing software you may find that using the soft eject works for
you. there may be data waiting to be written held in a cache and that is why
you can't open the drive.
third party software such this freeware app can unlock a locked drive
http://www.alexnolan.net/software/driveman.htm
Select the CD device and right click. select Unlock. However you may find
that you are forced to reboot.