New Wave, if we shall call this movement by this name, simply got assimilated into the mainstream (commercial elements of it) or pushed back underground (all the rest). The term certainly wasn't used since the mid 1980s - I remember my astonishment while reading a late 1986 review of Wang Chung live show in LA where they were crticized for still retaining "punk elements" to their sound and look. Wang Chung - punk?!! But there you go. Sigue Sputnik also proclaimed themselves punk, not "New Wave".
As for synth-based music, it was certainly seen as an acceptable commercial formula (speaking of Europe at large). PSB weren't considered "New Wave". Silent Circle weren't "New Wave" at all, it was just a German take on Italo Disco (I personally like them, but AFOS-imitating haircuts don't constitute "New Wave"
). Belouis Some were seen as a dance act - and so on.
In fact, from what I've read, the music that had some sort of legacy from "New Wave" era, disperced into dance (more synth-based acts) and "modern/alternative rock" (guitar-centric) scenes. I have a feeling that "New Wave" as we use it is a later, retroactive all-encompassing term from the 1990s - but even that is sometimes stretched to 1986, but not much later. So no point describing late 1980s music as "New Wave".