Does it happen every time? I'm pretty sure I've had it happen occasionally, but certainly not every time.

I often use the reverse thrust to back the C-130 out of a Parking/Cargo Ramp, but it never shuts the engines down.

I have been experiencing the same thing.  I never had this happen on an older computer that failed around February.  I replaced it with a new Dell XPS and installed all my previous programs including FSX and its addons.  On this new computer the shutdowns occured after every C-130 landing.  Today I repeatedly experimented with reversing while on a runway using a Saitek Aviator joystick programed to use one of the switches for the F2 (fast throttle reduction) command (the same set up I have used for 4  years).  Only the throttles moved, never the condition levers. I have used this  set up since activiating the new computer,  on other CS products and other addons for reverse thrust with no problem. Today the C-130 seemed to responded correctly to repeatedly reversing on the ground.  I stopped the reverse movements by momentarily advancing the throttles bringing the engines out of reverse and the engines continued running.  I then performed multiple approaches and landings using reverse (activated by a switch on the joystick, not F2, but programmed to perform the F2 function) after touch down and the engines shut down every time.  I'm baffled and cannot find the variable that results in the shut downs.  The only obvious difference between the old computer and the new one is the old one had Windows XP while the new one has Windows 7.  I'm running FSX with Acceleration, just as I did on the old computer.

Two days ago I made 6 short field landings using a technique of going to full reverse upon touchdown using a joystick throttle and when speed on the runway reduced to taxi speed I advanced the throttle to flight idle, let the engines stabilize and then retarded the throttles to ground idle.  On 5 out of 6 landings I was able to keep all the engines running with this technique.  Yesterday I did a series of 5 short field landings using the same technique.  On 3 of the landings all the engines shut down, on one the #4 engine shut down, the others  kept running, and only one landing had all 4 engines running after my technique.  Thought I had a work-around to the glitch, but it wasn't to be.

IF the condition levers move anywhere towards the rear at all Ground stop will happen.

If it's any help, I had the same problem.
I used the F2 key to apply reverse thrust and the F1 key to cancel it.
Each time, all four engines stopped.

However, I found that if I use the F2 key to apply the reverse thrust but
use just a very small amount of throttle to cancel it, reverse thrust is cancelled but the engines do not stop.

I don't have any fancy hardware, just a keyboard and a venerable Microsoft Sidewinder precision pro that has seen better days.

Regards,
Nick

i have the same problem sometimes