Their comment was that it is currently working nicely, but it's getting difficult to make meaningful changes. What I assume this means is the code is complex, fragile and full of 30 years of hacks and workarounds.
Yes, that's generally the case with legacy applications this old. And you have to train staff to work on it - there isn't a huge pool of Model 204 expertise out there.
That doesn't necessarily mean that reimplementation is worth the risk. But with an application like this one - which is probably exposed to the whims of the legislature, for example, since it deals with government funds - I'd be nervous about the cost of maintenance.