Yes, DSL filters can deteriorate over time; depending on where you look/who you ask, I've seen that they should be replaced every 3 months, every 6 months, every year...I have no idea which of those is correct (I certainly wouldn't make it a habit of replacing my DSL filter every 3 months), but I do know that I bought new DSL filters a few months ago and they said right on the package that they should be replaced every six months for optimal performance.
That said, I would never replace the filters unless I was absolutely sure that the filters were the source of my problem; they're fairly cheap individually, but the cost can add up quickly if you have multiple filters in your house. I purchased new filters a few months ago because my Internet provider insisted that my frequent disconnects were due to faulty filters...but they stressed that just changing one filter wasn't going to be good enough -- they would *all* have to be changed. Since my filters were several *years* old, I figured that it was a fairly plausible explanation (and I confirmed online that filters do have a limited lifespan), but after spending over 50.00 on new filters, I was still having the same problem. It turned out to be a faulty modem, not a faulty filter, that was causing the issue.
I haven't really heard a lot of concrete advice about the symptoms to look for when trying to determine if your filters are faulty, unfortunately. Most people just say, "Change them anyway -- they're cheap and you should change them regularly regardless." The best advice that I've seen that *doesn't* involve blindly throwing money at something that may or may not resolve your issue is to test your connection speeds with and without the filter in place; if they're significantly faster without the filter, then it's probably faulty.