According to the data you posted, HWiNFO is gracefully terminated when the system is suspended.
This is most likely done by something else in the system, for example if HWiNFO is started using Task Scheduler, it might be set to terminate it.
I use the latest beta for debugging which was started from the Explorer.
The problem is not in the termination, but in awaking after the hibernation.
After the hibernated machine becomes awake, all sensor values are frozen.
If it is possible to automatically restart it after hibernation, it would be also a solution.
Currently I tried this (not in the debug session I've posted) on a task scheduler event, but this failed due to insufficient permissions.
Do I need to terminate it in behalf of local system account?
I can only comment on what I see in the data you posted and there I can see that when the system enters hibernation, something terminates HWiNFO.
Where do you mean the sensor data is frozen - in HWiNFO sensors window or in the Shared Memory perhaps?
To start HWiNFO via Task Scheduler you need to enable the "Run with highest privileges" option.