Hi and welcome to the site.
A responsive design is inherently more complex than a fixed-width design, therefore it is likely to be less easy to maintain. However, I would suggest that:
If suitably designed from scratch, the additional workload is modest.
More importantly, that is a false comparison.
A more accurate comparison is between a responsive design and separate PC and mobile versions of a site. Then the benefits of a responsive design are pretty conclusive.
As for ease of maintenance, that depends on how the site is built, what you include in the term "maintenance" and who is maintaining it? Sites built with CMSs and themes are designed to be easy to build and easy to do basic maintenance, e.g. amending the content. Hence their popularity amongst professionals and amateurs alike. However, the situation is very different when it comes to changing the page structure, adding new facilities and maintenance of that sort. Then what may be relatively trivial changes to a hand-coded site may be horrendously complex and error prone. That is simply because of the much greater size and complexity of the CMS-based site. Now, this is true for fixed width and responsive designs, but the greater number of circumstances that have to be taken into account, and tested for, may make a responsive design significantly more difficult to adapt and modify.
However, much of this is surmise, because I'm not sure how many major responsive sites have reached the point where they need non-trivial maintenance. So it may be that the jury is still out on that one. And, in any case, I'd suggest that responsive design is here to stay. So if the current crop of responsive CMSs and themes prove difficult to maintain, then it is likely that they will be adapted or replaced by better ones.