I notice that this is old thread, but I, too, would find a non-breaking slash character handy, along with a non-breaking period/full-stop/dot/whatever you want to call it.
The non-breaking period seems to be an easier case. If the problem is a leading and/or trailing space, use non-breaking spaces (Ctrl-Space).
Slash is tougher, and I solved my one instance of it by using a completely different presentation, requiring no slashes.
But in experimenting, I found that an italicized or oblqued "|" would not break, nor would a math "fraction" (\xda). If I were using either hack, I'd be tempted to put the whole mess in a variable, say char.sym.slash.NB.
Another approach might be to find a comparable glyph in some non-Latin region of Unicode space. I need to stay 7.1-compatible, and didn't explore this.
It appears that the normal slash character is being special-cased for line breaks, and is always used if needed for line breaks, even if surrounded by non-breaking stuff, and even if Hyphenation is turned off.
One has always been able to turn off the line-breaking at a slash character by removing it from the Text Options panel "Allow Line Breaks After" item.
A feature I'd totally forgotten about. Thanks for the reminder.
However, that TO setting turns it off for the entire document, and the basenote did say "I'd like to be able to allow line breaks at slashes in some instances and suppress them in other instances".
It would be nice to have the equivalent of the non-breaking space and non-breaking hyphen, or more generically, a non-breaking tag that could be applied to any run of text.