I had assumed that this 1 hour gain occurred every time it resynced with exchange. However, I had been continuously connected for days on end and it still happened.
Upon further examination, I discovered that each 1 hour gain occurred on the daily "anniversary" of the time that it was last rebooted, e.g. I rebooted router at 16:00 on 2 May and at 16:00 on 3 May the times in the log increased by 1 hour, including the log event of the original resync yesterday.
Maybe it has something to do with falsely correcting for Daylight Saving Time every day, but I'm sure I've seen it in the winter. Let you know next Oct!
Note that is not just the times in the log subsequent to the increase event that are increased, but all the times in the log are increased by 1 hour every day at the same time as the BrightBox was originally rebooted.
However the "Time Connected: " in the top Status page is not increased and is always correct.
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 20 Meg WBC