Is there a relationship between pronouncing the final "s" and being a negative context?

There are actually rules that specify in which context to use which pronunciation of plus. One such general rule is that, indeed, in a positive context you pronounce the -s and in a negative one you don't. There are a few other rules plus the case of a liaison with the next word (if that starts with a vowel).

Rather than duplicate what's available online, I'll refer you to a page I found helpful (there's also a worksheet to test your knowledge at the end): http://frenchyourway.com.au/how-to-pronounce-plus-in-french