It's happened on every android device I've owned (and others, friends/families I've used to see if their's has the issues too). I've had everything from the OG droid through to now having the RAZR Maxx HD (mostly moto's, but some Samsungs and HTC's in between...I switch phones a LOT).
Basically if you're a fast typer (both thumbs) and you rely on autocorrect, as I do, go into a new text, email...anything really that will allow you to just type away...and just start typing, maybe try typing in a page or two of a book or something as you're reading it (just an idea to get the "length" thing going). IT HAS TO BE LENGTHY AND FAST TYPING FOR IT TO HAPPEN. Last lengthy thing I did that it happened with was 370 words and 2,000 characters (roughly). It was completely unusable by the end.
Anyway, over time the keyboard response will just slow down, not noticeable at first, then seems a little "sticky" then super slow then unuseable.
Being that I've experienced this problem on at LEAST 15+ Androids I know it's not just me, it IS a problem with Androids - It's not possible that only the 15+ androids I've tried to replicate this on were the only 15+ androids in existence that have this problem...If that were the case, I'd be winning the lottery every week.
By the way, I did try swiftkey3, had the same problem.
As for whats running on the phone...Doesn't matter because I could go from a factory reset phone, setup NOTHING, open an existing on phone app to type in, text messaging, whatever and experience the problem. But just for the sake of argument, I don't leave anything running on my phones, advanced task killer is set to aggressive and kills everything every half hour, the only other things I use are email, text, phone, web browsing etc...