I've been using DVD Shrink for about 6 months with no problems.
I've burned about 50 DVDs. Now the last 5 DVDs I've tried have
failed in the burning process, a box pops up tells me what kind
of equipment I have but not realy what happened.
You could try AnyDvd, it's a driver that runs in the backround while using Decrypter or shrink helping them crack the copy protection and produce a backup. It comes with a 21 day free trial before you have to buy it. All you have to do is install it, reboot, insert the DVD, run shrink as you normally would, anydvd will do it's thing without any user input.
If you haven't changed your media recently, or your burning application and write speed, it could simply be just a bad batch of disks (it's not uncommon to get 2-3 bad disks in a row, it's happened to me). Try another disk and see what happens.
You might also want to check and see if ther's a firmware update for your burner, if so update the firmware. Firmware updates add additional media support as well as enhance performance.
Here is a link you can use to check and see if a firmware update is available, just enter the model# in the search field, if an update is available just click on it to download.