It would be disappointing to go to great effort to replace the plurality voting system with an improved system – only to see the rules changed to go back to plurality again!
Historically, that has happened with Approval Voting (see #12 there, or just read on here). And it has happened with IRV voting (read on) and proportional representation (PR) systems. But, as far as we know, there has not yet been any instance of a backslide from range voting to plurality or anything else. Let us look at these in succession.
Approval voting in the IEEE: The IEEE (Institute of Electrical and Electronic Engineers – world's largest professional organization, comparable in clout, money, and membership to some small countries) adopted approval voting in 1987, but then backslid by restoring plurality voting in 2002. Why? Their claimed reason was the large percentage (80%) of IEEE members who voted plurality-style. [See the IEEE newspaper The Institute 28,4 (Dec 2004) page 5 (right bottom).] Now one can debate whether these stated reasons of the IEEE make sense. While I personally disagree with the IEEE backslide decision, I think their reasons do make some sense – why adopt a more complicated system if most voters will not use it? (Answer: because when they do use it, it can matter.)
In contrast, our studies (paper #82 here) show with range voting, only a small percentage vote in plurality style (about 19%). So: the IEEE's rationale for backsliding will not be available with range.
See also the low down "politically incorrect" theory of why the IEEE really did it.
IRV voting (and PR) in USA cities: Many US cities (most famously, New York City in 1936; also Cincinnati) adopted either IRV or STV-type proportional representation (multiwinner) elections in the 1930s. [STV, in elections with only one winner, is the same thing as IRV.] (Also the Louisiana Democratic Party adopted top-2-IRV for its gubernatorial primary elections.) Almost all of them, including all three mentioned here, later changed their minds.
More recently IRV has been re-introduced in the USA in a lot of places, and the voters in those places in many cases then repealed IRV after 1 or 2 bad experiences using it, e.g. Burlington VT, Aspen CO, Cary NC, Pierce County WA, etc.
Approval voting at Dartmouth College: Dartmouth adopted approval voting in 1990 to fill vacancies as they arose on its "Board of Trustees." But as of 2007 , it appears from this report (pdf) that Dartmouth is about to abandon it to go back to plurality voting. Why? See discussion. We suspect that the Dartmouth voters would be less likely to countenance e.g, abandoning choosing valedictorians via grade-point averages and switching to "each professor names one student" plurality voting. (Well, we know they would be less likely, since count the number of years this system has been operating without any such proposal.) In other words, range voting would seem less likely to lead to a backslide. Meanwhile, the Dartmouth undergraduate student government was elected using approval voting, at least during 2010-2013, I'm not sure when it first was adopted.
Range voting: So far, no organization I know of that has adopted range voting (e.g. the olympics, internet movie sites, internet recipe sites, schools that use 0-100 grading on tests, honeybees) has ever rejected it and gone to plurality voting [or approval, or IRV], and indeed, the self-evident quality advantage of range for them is so immense that it would probably seem ludicrous for them even to consider doing so – i.e. they do not even consider it.
Moral: The lesson of the historical record (small though that record may be) so far is 100% clear: range always stays once it gets adopted – but approval and IRV often do not stay.