I just finished installing SP3 and trying to update to RU6 using the same admin account. It's failing and rolling back on both our servers. Event Viewer says:
Product: Microsoft Exchange Server - Update 'Update Rollup 6 for Exchange Server 2010 Service Pack 3 (KB2936871) 14.3.195.1' could not be installed. Error code 1603. Additional information is available in the log file c:\ExchangeSetupLogs\rollup.log.
I ran it again and logged the process. I can't seem to find a clue in the logs though. The log file is large so I can't paste it here but I've posted it here: https://onedrive.live.com/redir?resid=BA13E92AD70E1535!244&authkey=!AAdjDtNao_v0pL0&ithint=file%2c.log