[Michael Juster]

Does anyone know the technical term for a verb that combines past action with ongoing action: e.g. "the water keeps on flowing" or "the politician keeps lying"?

As always, the good Doctor will assuredly be grateful for assistance.

[E. Shaun Russell]

Predicate nominative gerund, I believe.

[Bill Carpenter]

This commentator considers those "gerund complements." http://www.grammar-quizzes.com/gerund2a.html

[Max Goodman]

I cross-posted with Bill, who has probably answered Mike's question.

[Julie Steiner]

The use of "to keep" instead of "to be" as an auxiliary in the present progressive might not be an exact parallel with the suffix that forms frequentative verbs in Latin, but that crossed my mind.

I thought this might be helpful, too, but it doesn't seem to be. Then again, maybe it is.

[Ann Drysdale]

Anything that introduces the element of past establishment of the action to the present continuous (progressive) tense of its ongoingness has to help us towards the good Doctor's druthers, eh?