A search of the Hansard Corpus turns up an 1803 example:
Can the right hon. gent. I will ask, pretend to maintain, that those circumstances were by any means so strong as the present time offered, a time when invasion is impending and disaffection is actually existing in Ireland?
And in 1812, by none other than Lord Grenville:
That this danger is now existing: Four millions of your countrymen have been born and educated in this religious faith, and not even our ministers themselves have yet proposed to us the forcible conversion of that great community.
You can find plenty of examples of it in the twentieth century as well, though this usage fades relative to the participial usage.
Naturally, some such responsibility for decisions must fall upon an individual, but this is a machinery which is existing, which has existed for years, and which has worked satisfactorily (Auckland Geddes, 1918)
At this point, I started to wonder if Parliament ever debated anything besides Ireland, and then I found
I can assure the hon: Lady that nobody is being detained unless that is necessary in the interests of safety in the present conditions in which Cyprus is existing (John Hare, 1956)
There is already existing here a web of financial incentives for film production in Europe. (1995)
As for American English, a COHA search also turns up examples of existing in the progressive going back some ways—
It is hardly necessary to add to this incontestable statement the further fact that the new President, as well as the citizens through whose suffrage he has come into the administration, has always repudiated all designs whatever and wherever imputed to him and them of disturbing the system of slavery as it is existing under the Constitution and laws. (Old Guard, Mar 1867)
[F]or in this world is existing the infinite fullness of the Divine Mind, open in all its limitless affluence to every soul… (A Textbook of Theosophy, C. W. Leadbeater, 1925)
and COCA finds a few in recent use, though more in spoken than written sources:
She's an innocent yet fully formed adult clone named Jordan Two Delta, who was born as an adult, given select memories and now is existing in a secret clone colony without any knowledge that she's really "just an insurance policy." (Chicago Sun-Times, 2005)
The facade the only thing that still is existing now. (CBS Early Show, 2011)
This satisfies me that progressive existing does exist, and isn't ungrammatical, but also that it is unidiomatic, particularly in modern written English.