I'm asking this question because current modern Spectroscopy machines, which are fully based on digital electronics can become obsolete or their upgrading is extremely expensive everytime there are particular OS updates or OS upgrades.
it depends on whether the dedicated computer needs access to the internet to function. If not, it can operate stand-alone and should function as long as it lives. We have done this many times in the past to become insensitive to network failures during lengthy experiments. The only problem may the keeping the time correct as there is no means of synchronization.
Sometimes, the dedicated software has a service limit built into the program: it may stop functioning beyond that limit. One usually fixes that by bringing the system's time to an earlier date. This may be tricky though as software manufacturers may anticipate this solution.
My guess is that manufacturers may not have a big interest in producing their own OS for their software, especially not when it means that the user may not need (paid) software updates in the future.
As Ger suggested, you may use an offline computer system with a stable OS version and use it as long as it runs and replacement hardware is still available. However, this may become an issue in 5-10 years.
My suggestion is to use virtual machines, install all necessary software into the VM and run this VM on a modern machine. You are able to restrict network access to the VM for services you deem necessary. You may also backup the VM or copy it to a new, more modern, machine so you can have (a) backup and (b) are independent of hardware and consequently driver support. For the longterm you should choose a VM solution which is open source and may therefore be supported also in the future. There are VM solutions for servers, but maybe Virtualbox may do for most end-user needs?
I agree with the above two answers - keep the computer offline. Many of the updates may be security updates. If the old dedicated computer hardware "dies" then you may be able to operate your old version of the software by using a virtual machine running the old operating system (eg Windows 2000). You will need to talk to your IT department as to how to set this up.