Decay issues come from excessive response - it's not so much that the driver is still vibrating when it should have stopped, rather the problem is that if there's something wrong (relatively more than absolutely) with the response, you can effectively hear longer decays. Let's take bass for example - when the bass instead of "THUDTHUDTHUDTHUDTHUD" or "dum dum da da dum" turns into "THWAAATHWAAADTHWAAADTHWAAAD" and "duwooduwooomdwaamdwaamdwooooom" it's not that the diaphragm is vibrating excesssively, but that the response has too much low bass and not enough (even in relative terms) of the upper bass, you just don't hear the next note properly. In effect, it's not actually that THUDTHUDTHUD has no extension in the decay (I mean, really, sit next to a bass drum and have someone give the pedal a good kick), it's just that since the upper bass response is relatively strong or are both relatively even, you hear the next THUD while the decay of the previous THUD is gradually and quickly dissipating (as opposed to being too loud). You can test this by adding, say, a +10dB bass boost at below 80hz (but doesn't affect 120hz and up much) on a headphone that sounds "fast." Conversely, one may encounter a headphone known to be "flat" and then its bass drum sounds more like a snare with a pillow stuffed inside - that's because the headphone may be generally flat but then the low end response drops off early (like, compare some 5in stand mount speakers to a tower speaker with three 6in drivers).
If you look at the graph of the HD600 (and barring how accurate these should be in reality, when not taken with a mic inside a skull encased in ballistics meat, with a simulated ear canal shape going to the mic/s) there'a plateau in the bass response up to well above 100hz. On brand new pads this is absolutely no problem, especially with powerful, clean, neutral amps. However, use an HD600 with squished, worn out earpads (that exacerbate that bass response as the drivers are closer to the ears, and the earpads are effectively sealing in more bass), and even with a neutral amplifer and source chances are the decay issues (which is actually a frequency response issue) will be audible.