I don't think it's fair to say languages "typically" lose complexity over time. If that were the case, we wouldn't have loads of languages with all kinds of complexity very much in full swing.
The loss of complexity is common, that's true. But from what I know, it needs some kind of push to get going, it doesn't just emerge on its own. Much like the great vowel shift in English started with one vowel being changed in fashionable speech of fashionable people, and that vowel then pushed the other vowels out of its way, because otherwise there would've been too much overlap.
And sometimes apparent loss of complexity leads to a different kind of complexity emerging, like for example if the sound system is collapsed so that you have a lot of homonyms, you now have a complex system of homonyms to deal with.