I think iterative fits best, although durative is another possibility. The verb keep can express iterative and/or durative aspect, meaning that it indicates the repetition of an event or action that persists. Iterative and durative are listed as an aspect in the Wikipedia article.
Looking at that article, however, the number of aspects that one needs to accommmodate all the various morphological and lexical mechanisms across languages that can express what we broadly construe as "aspect" is very large. My assessment is that the science in the area is not exact, nor can one expect it to be exact based on all the nuances. The grammarian therefore has a measure of freedom in the nomenclature he/she employs to denote the aspect at hand. The particular inventory of aspects posited is likely to vary from one grammarian to the next.
The situation is no different in other areas of grammar. The inventory of semantic roles (thematic roles) assumed varies from one grammarian to the next. The inventory of adjunct categories (causal, concessive, temporal, manner, etc.) also varies from one grammarian to the next. Why should it be any different for the inventory of aspects that the grammarian posits?
There is, however, a more concrete way to approach the classification of a verb like keep. It is not an auxiliary verb, since it does not license subject-auxiliary inversion or VP-ellipsis, nor does it accept not as a postdependent:
a. He kept laughing.
b. *Kept he laughing?
c. *She kept laughing, and he kept, too.
d. *He kept not laughing.
Hence keep is unlike have of perfect aspect, which is a clearly an auxiliary. Keep is, rather, a subject-to-subject raising verb like begin (She began helping), quit (He quit eating), start (You started drinking), and stop (They stopped protesting). See the aticle on raising here: https://en.wikipedia.org/wiki/Raising_%28linguistics%29. This class of raising verbs takes the progresssive participle as complement. Each of these verbs expresses aspect: begin and start express inchoative aspect, stop and quit terminative aspect. As a class, they might all be called aspectual (subject-to-suject) raising verbs.
In sum, keep is an aspectual (subject-to-subject) raising verb that expresses iterative/durative meaning.