This question has three parts:
One, the very definition of autism dictates that children with autism suffer from a decreased rate of development in many areas, and even regress a little in others. So the answer is, yes, children with autism regress.
Two, a particular disorder on the spectrum is Crie Du Chat Syndrome, which only affects little girls. In this case, girls develop at a completely normal rate like all other autism spectrum disorders, but the syndrome strikes them much later on than autism normally does. They may appear to be completely normal little girls one day, and start some very odd behaviors the next. Tests for missing chromosome parts confirm the presence of the syndrome, and nothing can be done to stop it once it starts. The girls rapidly regress almost to a newborn state, not being able to speak, perform daily skills, or even take care of their own toileting needs. In this case, again the answer to the question is, yes, children with a specific type of autism spectrum disorder regress.
Three, children with situational problems will often regress, with or without autism being a factor. These cases are very sad because the child has been abused, or because they have suffered some extreme trauma for which help was never sought. In these cases of regression the child with autism will regress, even after lots of hard work to gain skills that were functioning normally. It will be very obvious and the decline is noticeable within a month of the trauma or the start of the abuse. Good record keeping of both the progress in the developmental areas of focus and the sudden onset of decline are vital in showing a doctor that something is wrong.
One final note on this matter: children with other types of autism can learn, grow, gain new skills and lead fairly normal lives without ever losing the skills they obtained. Practice of those skills regularly keeps the memory muscle strong. Not practicing them will look like a regression, when, in fact, it isn’t. High functioning autistic kids do not regress, although emotionally they struggle to behave at a level that fits their chronological age. Usually only additional brain trauma with lasting effects will cause a child with autism to regress, and obviously, that’s with “good” reason.
Ergo, the final result of this question is, yes, in some circumstances they can and do regress, and no, most high functioning or mid-level functioning autistic kids do not regress. If this were a question on a science or child development quiz, it would be viewed as a trick question for all of the above reasons.