Thanks to all for their help. I had previously tried restarting to no effect, but I did it one more time (thanks, HIHZia) and yielded one successful burn then 3 bad burns in a row. So I called Humax and was given a no-hassle return offer with two options -- send the unit back and they would replace it, or keep the unit until a new one arrives (they put a $500 credit card hold to be released upon their receipt of the faulty unit within 30 days). I opted for the latter, with the new unit supposed to arrive within 7--10 days. I must say I'm impressed since my unit is out of warranty.
There are several shows I have saved on this unit that I would like to burn to DVD, but I believe there's a way to transfer them to the new unit when it comes and then burn them from there, yes?
Thanks again to all who offered help. What a great bunch!