The design was started in 1974. The first unit was complete in 1981. See this report. Note that they underwent a major change around 2000, which took 4 years to undergo all of the remaining suits. While it seems like some components of the EMU suits were recycled, many of them were not, so in many ways it is a new design.
I can't find the date the last of these was built, but I assume it was in the early 1980s. So 40 years is a bit of an exaggeration, but 30+ years is certainly the case. From the list of space suits destroyed, it would seem they manufactured them in the 1980s and have been upgrading them since, particularly since of the 18 space suits mentioned, 2 were destroyed on Challenger.
Also, they can be stored on the ISS for up to 6 years, or 25 EVAs, whichever happens first, after which time they need to be brought down and refurbished.