I've been having the same issue as the original poster, but do not have 'require user input' enabled on my YubiKey NEO.
The relevant events are listed below.
Every time this has happened for me has been after resuming from sleep, plugging in my YubiKey, and logging in. After this I get a 'Windows has encountered a critical problem and will restart automatically in one minute. Please save your work now.' This seems to happen to me about 1/3 times, and is not so easily predictable.
I do have the windows error report dump if that helps also.
For now I've had to disable using the YubiKey to authenticate my Windows user, as set with the YubiKey Logon Administration tool.
Any help appreciated, as right now this functionality is useless with crashes like this.
Event 1000, Application Error
Code:
Faulting application name: lsass.exe, version: 6.1.7601.18443, time stamp: 0x5348920c
Faulting module name: YubiClientAPI.dll_unloaded, version: 0.0.0.0, time stamp: 0x548145f2
Exception code: 0xc0000005
Fault offset: 0x000007fef57116c9
Faulting process id: 0x3b4
Faulting application start time: 0x01d0f5603544f107
Faulting application path: C:\Windows\system32\lsass.exe
Faulting module path: YubiClientAPI.dll
Report Id: ca95cda5-62f5-11e5-96a1-005056c00008
Event 1015, Wininit
Code:
A critical system process, C:\Windows\system32\lsass.exe, failed with status code 255. The machine must now be restarted.
Event 6008, EventLog
Code:
The previous system shutdown at 12:53:22 PM on 24/09/2015 was unexpected.