Ninjas offered in Great Plates do tend to resurface for a couple weeks afterwards, whether it be offered in another F2P way such as: 3v3 arena, recruitment benefits, myoboku trial. Speaking from my own experience, this It is not guaranteed, but still a high chance nonetheless.

This was the case with Yagura [Tree Tails] and Tobirama [Swimsuit]. So if you see that ninja offered in Great Plates expect to see him some more very soon.