There are several issues here, but all related to folding/unfolding parachute mechanics.
First of all look at the unfolding of the cargo parachutes in the following video:
All parachutes in the video are created with "FLY" attribute (code: http://killzonekid.com/arma-scripting-tutorials-epic-armour-drop/) which means they should be already open when created, and this is how it is indeed if you try it in the editor, but on dedicated server, where this video is shot, they go through full cycle of animation.
Another problem is with folding of the parachute. The folding animation starts when isTouchingGround returns true, i.e parachute is on the ground. However if parachute bounces for any reason or lands on a slope where it slides and appears above the ground again, it unfolds again and this could be going on for a long time. I have constructed a script that would simulate this and here is the result:
What is also interesting, after the parachute is nudged up once by the test script, it gets also nudged up twice by an unknown force.
Solution? Make folding of the parachute terminal, i.e. when the folding is started, that's it, it cannot be cancelled. At the moment for some reason the status of the parachute above the ground is checked constantly. It would also be more optimal to stop these checks once the parachute has touched the ground once and folding started.