I have been at many places, in many teams, where no-one has ownership of the build scripts. It’s an area where a company can bleed a vast amount of time and money without realising it. It may even be what makes senior member leave in the end due to frustration with to much inaction.
What is unfortunate is that it is relatively simple to fix. Sure, there are risks associated with any legacy clean up. But getting the build to work is far simpler then many other tasks in a legacy codebase. I find that the main reason it is not done is that the team can't communicate the value to management (including product owners). Therefor it gets low priority and ends up at the bottom of the back log.
I have always found that one of the best ways to communicate value to management is in money. By putting forward a business case with a clear RoI (return of investment). When it comes to build scripts this is a pretty easy task. First, ask everyone on the team who uses the build scripts to keep track of how much time they spend doing build related stuff. How much time do they spend working around a broken or non-functional build. Try to count only time which is spent unnecessarily. Once you have enough data to know what the broken builds costs on a weekly/monthly/quarterly (which ever suites your needs) basis it is time to look at how much it will cost to fix the build. I suspect the ratio will be quite scary. The difference is how much you loose each week/month/quarter. Hopefully this should get managements attention and priority.
Now that fixing the build is top in the backlog we need to make sure it doesn't fall back into despair again. This is where ownership comes into play. In a well functioning self organising team this is never an issue. Everyone owns the build. Everyone makes sure the build is just as snappy as everything else.
But If you don't work in senior or self organising team? Who should be responsible? A good place to start is the team. Perhaps someone feels very strongly for it. Passion goes a long way. Granted, you can't have just one who owns the build. It is knowledge which is far to important not to share between at least two. But with one lead it's usually easy to follow. Make sure to pair often to distribute knowledge.
If it's difficult to find someone who wants to take responsibility the team should make sure to pass it around. Share the pain to make it lesser for everyone. The main responsibility will however always fall on the architect. A working build is part of the non functional requirements that makes up an architects main concerns. How will you as the architect be able to guarantee that the solution you are the master builder of will ever reach it's intended user or customer if it cannot be built?
Now, go and fix that build and remove the pain. It is so worth it. And remember, with a working build you'll have so much more time to code, and that is what's really fun!