"Persistent" can be defined as "continuing without change in function or structure," which when you really think about it doesn't quite fit with how it is employed in most MMORPGs. Many MMOs claim to have a "persistent struggle," or "persistent world," which is only half true. Developers are constantly changing their MMOs and it impacts how we play.
What happens at the end of an expansion cycle? Often, players stop trying to progress and wait for the new content that makes old content obsolete. What happens when classes undergo constant balance shifts? Players are forced to compete on uneven playing fields. What happens when some gamers benefit from bugs or exploits before they are fixed? It can hurt player morale.
Many of these changes are for the best, but it does illustrate that MMOs are not truly as persistent as they claim.