For example, we see the loss of cases and endings in the Romance languages vs. Classical Latin, and even in Classical Latin vs. Old Latin. The same is true in Modern English vs. Old English.
Perhaps the real question is: why were they so complex to begin with?
I think the assumption of your question is problematic.
You may want to try the specialists over at http://www.reddit.com/r/linguistics/ . They will probably tell you that grammar isn't less complex, just the forms of complexity have changed. For example, English has invented grammatical stuff that wasn't in Classical Latin, but Spanish has retained some of Latin's cases and declensions. Frankly, I don't find Spanish to be more complex than English, and in fact in some ways it's more versatile for being an inflected language.
Yes, ask in /r/linguistics. You are only observing the loss of some forms of complexity, but languages also develop complexity at times. Language in general doesn't necessarily go from more to less complex.