from The Century Dictionary.
- In an unremitted manner; incessantly; continuously.
Sorry, no etymologies found.
But owing to the successive collapses of her rivals, she now found herself not only forced to attack as the safest course of action, but driven to the view that the Power that exerts the maximum pressure constantly and unremittedly is inevitably the most successful.
The Fight for the Republic in China Bertram Lenox Simpson 1903
For, besides his complaint, first stated, of having never possessed their confidence, in a late letter  (in which, notwithstanding the censures of Parliament, he magnifies his own conduct) he says, that, in all the long period of his service, "he has almost unremittedly wanted the support which all his predecessors had enjoyed from their constituents.
The Works of the Right Honourable Edmund Burke, Vol. 08 (of 12) Edmund Burke 1763