It’s an often-told story: A portmanteau word (useful or playful or both) invites other portmanteaus sharing an element (usually the second), and then these drift from the phonology and semantics of the original to such an extent that the shared element takes on a life of its own — is “liberated” as an affix. Some examples follow.
-dar: gaydar ‘ability to detect that people are gay’ (gay + radar, the second historically an acronym) motivated a pile of other -dar portmanteaus (Language Log discussions here, here, and here), so that eventually -dar came to be seen as a formative on its own, usable with bases other than monosyllables (from jewdar and blackdar, eventually to humordar and sarcasmdar) and conveying not just ‘ability to detect people in some social group’ but more generally ‘ability to detect some quality’.
-nomics: The story of -dar is parallel to the way -nomics (originating in economics) broke free, through the mediation of portmanteaus like Reaganomics and (especially) Freakonomics. (Meanwhile, -omics is on its way, from genomics, via portmanteaus like culturomics; discussion of both here.)
-tini, -kini, and -zilla: These are at various stages of liberation, furthest for -zilla (based on Godzilla), less for -kini (based on bikini) and -tini (based on martini). Discussion of the -ini formatives here, -zilla here.
-cation: Now, going back a bit, there’s -cation (based on vacation), here.
At first, -cation, as in staycation (stay + vacation, ‘a vacation in which you stay at home’) was pretty closely tethered to its roots. But then the first element diverged phonologically from monosyllables, giving things like seniorcation and Eurocation. And its second element generalized semantically, to anything having to do with vacations, as in kidcation ‘vacation from kids’. This isn’t all the way to a fully semantically generalized -cation, which might mean something like ‘absence’ or ‘break in routine’, but it’s on the way.
In any particular case, the question is whether speakers see themselves as combining two words (in a portmanteau, essentially compounding with overlap) or as combining a base and a suffix-like element (in libfixation). Probably some people go one way, some the other, and some change over time.