They started rolling out in 1989 yes, the 'newest' full car (Excluding those put together from parts of crashed cars) went online in 1991, so they'll have been in service for 30 years next year.
In comparison the Mark IV they replaced were in service from 1971 to 1989 (18 years).
Its worth noting as well that age wasn't the primary reason of the Mark IV being replaced - they were a fair bit smaller and Disney had to start adding an additional car to get a bit more capacity out of them. That being said the two youngest cars were only introduced in 1984 so were only used for 5 years! They did get a new life in Las Vegas and were in use up until 2004 (20 years).
In the grand scheme of things the monorails are not that old. They are just the oldest fleet Disney has had. If they were correctly maintained (and given real refurbishments, not a quick wipe over and some crappy new carpet on the walls) they'd have lasted another 10 years. But because Disney cut corners we're left with crappy old monorails that have lost their prestigious reliability score of 99.985%
Give it time, they'll be replaced. Till then expect more screwups and more incidents.