Is this how Duolingo is supposed to work?
As I am progressing through lessons, I tend to fail every lesson about 5-8 times (sometimes many more times, depending on how hard the lesson is, such as the adverbs section of German) until I essentially memorize or remember each translation or answer. I was wondering if this is how I am supposed to be learning these lessons? I find it a bit hard to get the grammar correct when translating sentences because there is little explanation, just word hints. Do other people go through this same process of failure?
Yes, same here. The thing with Duolingo is simple: "We are going to make you use the same verbs/words/expressions a lot of times, until they will be stuck inside your brain. In this way, you will learn new things without even noticing". In fact, if you try to re-do the old exercises you used to fail, you will very hardly make mistakes, since the grammar rules in which they are based are well memorized inside your brain. It is normal to fail the lessons different times, but everytime you try again, the mistakes will be less and less, and eventually you are going to get it right. At that moment, you will embrace that specific grammar rule, and since you've used it so many times, you will never forget it.
(tl;dr - learn grammar outside Duolingo)
I'm not learning German, so maybe my answer is irrelevant to this specific discussion, but I don't think failing a lesson 5-8 times until you memorize each translation is the right approach. Of course, the more "exposure" to a concept, the better, but there are usually clear explanations available online about grammar points or nuances, especially for the languages currently covered by Duolingo, as they are among the most common attempted by English speakers.
I think Duolingo could definitely do a much better job explaining certain aspects of the grammar, but where they are lacking, the rest of the internet or a good grammar book easily fills in the gaps. I find that when I make a mistake, if I understand the reason behind my mistake, I tend not to make the same type of mistake as much, or if I do, I can identify where I screwed up. It's much more fun for me if I can apply grammar rules to the lessons instead of brute forcing them until I memorize all the phrases contained within them. Seeing the owl cry over and over is a little discouraging!
That said, it could be that German is simply harder or that this approach is working for you. But the idea behind learning a language is to be able to communicate in it and that extends beyond regurgitating the limited number of phrases on Duolingo. Vocabulary must be memorized, but grammar rules should be learned and applied. As a very basic example, if a learner never takes the time to understand cases in German, they would struggle with the simplest sentences, even after they've accumulated thousands of vocabulary words.
Since I'm learning Spanish, my resources are mostly for that language, but the French about.com pages are very useful, so maybe the German ones are too: http://german.about.com/library/blgrammatik.htm
But hopefully someone who is actually learning German will be able to point you in the right direction. It's no fun to solely focus on grammar either; I just really think understanding why you make the mistakes you make improves your learning and your confidence.
Sometimes I think D learning is like babies learn-what I mean is they don't get grammar from the cradle just here simple things over and over then more complex and one day they catch on. Yes, I'm doing a lot of failing but have found to my amazement that there are times I actually "get" something without strugglling. Oh but I do use some outside help: I love this site: http://www.nthuleen.com/teach/grammar.html the "Handouts" are awesome.