It should work fine, given that you are using DVD-R in both instances. You shouldn't need firmware upgrading.
However, I've had a look and there is a later version of firmware out available here
but you want to make sure you've got the right one. Also read the warnings - it is possible to turn your DVD drive into landfill if it doesn't work out. Do so at your own risk!
My first question is: How many discs have actually failed? Does it happen consistently? If it happened once in ten or whatever it might be a bad batch of media.
Also each DVD burner has specific parameters in terms of burndepth, duration and so on. The same goes for DVD discs. Unfortunately the two don't always match up, meaning some writers don't jwork well (or at all) with certain brands. Add to that the batch variability of DVD discs even within the same brand - you can end up with a lot of drinks coasters.
I'm not familiar with the brand you're using, but I personally use Verbatim discs. The DVD+R were recently rated especially highly and I'm getting very few burn failures (but they can happen, for various reasons).
Let us know how you get on