I found an operator's manual on Kubota books.
I learned your tractor has an operator presence controller.
It reads this way to me. If you are in the operator's seat, engine running and pto engaged, then if the tractor thinks you have fallen off it will stop the engine in 1 second.
I also interpret this to mean if the pto is not engaged, then the operator presence control wont stop the engine.
Test: Switch for the operator's seat
1. Sit on the operator's seat
2. Start the engine
3. Engage the PTO gear shift lever
4. Stand up (Do not get off the machine)
5. The engine must shut off after approximately 1 second
6. If it does not stop go to dealer
The "does not happen in reverse," is not making me think of anything. Perhaps a more detailed description of when, and how this problem makes it condition known. Fuel tank full. Level ground or slope. You say not so much when warmed up. How cold outside is it when this happens
If you don't have an operator's manual, I suggest you download and read carefully so you can know if what you are experiencing is part of the design or a malfunction.
www.kubotabooks.com
The high low range shift is always touchy to get into a different range. I try and do it just before the tractor stops moving so the gears are still slowly rotating.
Dave M7040