Understanding spoken English like a native speaker: Do you think it's possible?

This question and discussion is aimed towards the advanced learners here, I would like some of you guys' input on this and I apologize in advance If this turns out to be too long in case you're not that much of a reader and I'm using English here because I'm actually more comfortable and able to come up with better words for the subject at hand this way. I've been focusing on my listening skills a lot lately and I've come to the realization that listening is a very hard skill to master when It comes to a foreign language. Anybody who is hoping to ever achieve native speaker level of listening comprehension in English is in for long ride, that's for sure. There's a lot of factors that make understanding spoken English to the maximum difficult but I'll try to narrow It down into the two main ones:

Combination of words you're not used to

It can be two words you first came in contact with years ago and you've known what they mean forever, but If they usually don't go together in a sentence right after one another then it becomes pretty much impossible for your ears to recognize that sound pattern right away, especially if it's spoken fast (and make no mistake about It, most English native speakers don't care for speaking slowly.)

Weak/non-emphasized words

I would say this is probably the hardest one. Do you know those little words like prepositions, pronouns, modal verbs and such which are the most commonly used words in all languages? You would think they are easy for your ears because they come up in conversations all the time and getting used to their sounds would be a piece of cake, right? Well, think again. They are actually the ones who for the most part will give you the hardest time when It comes to understanding spoken English. This is because native speakers tend to put emphasis on nouns and longer words and the type of words I mentioned gain very little stress when being spoken and go pretty much unnoticed. Add to It the fact that most people speak fairly quickly like I said, and it'll be HELL for your ears to catch those weak little words with ease (not all the time, It's mostly when people speak fast and unclearly, but unfortunately a lot of native speakers mumble their words and as fast as they can, so...)

So, do you think It's at all possible to achieve that level of mastery regarding listening comprehension? Have you met a non-native speaker who's been able to, or perhaps you've done it yourself? If so share your approach to it and how long It took you, we'd be happy to read It.