Well, logic suggests that there are objects in the artwork that have been assigned various spot colors. Spot colors would correspond to premixed, color-matched inks on press, as opposed to CMYK values. Illustrator is alerting you to the fact that it cannot save a file with more than 27 different spot colors specified.
There is probably a book to write on how amiss someone's workflow has gone, or how clueless they are about production, when they are sending their printer files with 20 or 30-some spot colors. And frankly, I suspect your own workflow is inherently a bit askew as well, as here you are trying to save a file with that many spot colors, although somehow it was saved before it got to you...apparently not in Illustrator. So I can only speculate that the artwork originated in some other application, perhaps arriving at your desk in PDF...(?)
Resolve it? You're a long way from the true roots of the problem, but if all you need is to save the file without getting an argument from Illustrator, try this:
Choose Edit > Edit Colors > Convert to CMYK
Disclaimer: the colors you print may not meet the expectations of the person who produced the artwork. Of course, it sounds like that could be the case with or without the conversion.
Not sure what type of equipment or technology you are intending to produce this work on but that not the issue here. I don't know of any limit to Illustrator spot color and have saved and printed jobs with more then 27 spot colors. The file may be corrupt, in which case have you tried a Save As with a different file name? If this doesn't fix the file you may have to create a new file in illustrator and copy and paste all content from the corrupt file to the new file with Paste Remembers Layers turned on in the flyout menu of the Layers Panel.
Also check if the color swatch names have any strange specialty, or Asian characters in the names. If so, change the swatch names so they are cleaned up. The last suggestion is to check any plug-ins you have active in Illustrator that might be involved in your workflow. I know there are prepress workflow plug-ins that have spot color limitations, like in Rampage.