In an unpublished manuscript of February 2015 I set out an account of the factors impacting the course of the profit rate, in a continuous time framework. I had intended to do this since my paper on the Okishio theorem but was not able to return to it until this point. For some reason I cannot remember, I never tried to publish it though I did place it on Academia and RePec. In retrospect this was unfortunate since the paper is a somewhat definitive statement, giving very precise algebraic conditions under which the rate will fall or rise.
I think that part of the reason I shelved it was that I had not produced, to my own satisfaction, a theoretically rigorous grounding for the continous time statement of the problems involved. I resolved this (to my own satisfaction, it is always necessary to state) in my paper on the ]General Theory of Value, Money and the State]
Having done that, and revisited this paper, I don’t as yet see any reason to drop or question its conclusions.