I used stack move command icon on lower right of the screen while an arty unit was selected.
*The game is C3C base game, no mods
*The stack was ordered to move 2 tiles, from a razed city to another city in order to attack. The whole thing happened overseas entirely on enemy territory.
*The stack moved correctly in the first turn but on the second turned that happened.
*only the arty disappeared and that happened during automove phase.
The nearest save is before the invasion, attached. The stack was landed near Hlobane, razed it while being reinforced by the arty in Persepolis, which was embarked at Sao Paulo and Rio Janero in additional transports, then marched 2 tiles towards Zimbabwe. The initial invasion force is where the Cruiser is. The disappearance happened during the march.
OK I downloaded your save and played a couple of turns -- admittedly not very efficiently, and I just hit 'ENTER' for all the build- and research-orders back in your homeland, fortifying anything that got built unless I needed it. I was unable to duplicate your disappearing Arty (although on the third reload, I did get awarded an SGL for AtomicTheory -- I built UniSuff, just for fun!).
Some saves are attached. First I landed your Cruiser-escorted stacks on the Tobacca-Hill south of Hlobane. With hindsight, this was not the most sensible place -- the Hills NW would have been better.
On the next turn, all the Arty was fired at Hlobane, redlining nearly everything in it. All Tanks were sent in immediately afterwards, killing the defenders -- the last one was promoted, and it razed the city. This is what I mean by 'inefficient' -- had I landed the Tanks directly adjacent to the city, I could have used half of them twice. Still, the Zulus then threw a lot of Rifles and LBMs (i.e. A=4 units) at the tank-stack outside Hlobane's ruins, and promoted each one of them (2 victories in the same turn).
The injured Elite-Tanks were then all retreated back under the 14-HP Cav-Army, which was left fortified in place. Two Arty were fired at a passing Galleon, redlining it, and the Cruiser then sank it (this was just bloodymindedness on my part!). A Transport then unloaded another 4 Arty onto the Tobacco-Hill.
The 13-HP Army, 2 vTanks, and the unfired Arty (10?) were ordered to stack-move 3tiles towards the Hill SW of Zimbabwe. THIS ORDER GOT INTERRUPTED DURING THE SECOND TURN, AND WHEN I USED THE STACK-MOVE ICON AGAIN, THE ARTY GOT LEFT BEHIND -- BECAUSE (I didn't realise) THEY HAD ALREADY USED THEIR MP.
At first I though that the stack had stopped moving because there had been a Zulu unit on the Hill, but I reloaded (twice, because on the first reload I forgot to unfortify the 13-HP Army before I ordered the 1st stack-move), and the same thing happened -- the stack stopped outside Zimbabwe. When I sent the 2nd stack (including the 14HP-Army, the Arty and the injured Elite Tanks) the same way -- it also stopped outside Zimbabwe, even though the first stack was already occupying the Hill.
So I checked your Game Preferences, and found what might be the 'problem'. You have 'Cancel orders for enemy unit' selected -- which means that stack-moves will get stopped when a stack meets an enemy -- including enemies fortifed in cities.
I am guessing that you might have done something similar to my first attempt -- tried to stack-move, and then did it again after the move-interrupt, leaving your guns unprotected. All Units are 'deleted' from one tile and 'redrawn' during moves, so the guns might have 'vanished' briefly as the Army moved onto the Hill, but they had actually got left behind...
), but 'U' on its own might not be obvious (yeah, like 'U235' is sooo much clearer... 
