I get the same experience as Bighorn. I can only make one clip. A subsequent clip overwrites (deletes) the previous one.
I am not using 365, but, certainly, nothing appears in Word 2016.
fwiw. I can only make on clip without saving. I guess we all have different combinations of settings. If I do NOT save, I am unable to make another snip.
I am not on the insider track, currently, but I understand they have reintroduced a useable clipboard which might take care of this?
I use a third party tool (snagit) which does allow the user to view and edit several snips. There are quite a few third party offers, some free.