The problem with that diagnosis, is that in this case, it's actually causing failures on the client side. The client in question has a flash game which pulls some amount of data over https, when these sessions time out and hand out a 408, it causes the game itself to barf up a lung. Additionally after pulling 12 hours of logs and doing UA matching, while Chrome on Win7 base seems to be the major player, we find these as well:

Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 6.0; Trident/5.0; SLCC1; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; .NET4.0C)
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.0; Trident/5.0; yie9)
Mozilla/4.0 (compatible; MSIE 7.0b; Windows NT 6.0)
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.0; WOW64; Trident/5.0; yie9)
Mozilla/5.0 (Windows NT 6.0; rv:11.0) Gecko/20100101 Firefox/11.0
Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 6.1; WOW64; Trident/5.0; SLCC2; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; Media Center PC 6.0; CPNTDF; .NET4.0C)
Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 6.0; GTB6; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618; WinNT-PAI 26.09.2009; .NET4.0C)
Mozilla/5.0 (Windows NT 6.1; rv:11.0) Gecko/20100101 Firefox/11.0
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; WOW64; Trident/5.0; NP06)
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; WOW64; Trident/5.0; SlimBrowser)
Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 6.0; Trident/5.0; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; MS-RTC EA 2; .NET CLR 3.5.30729; .NET CLR 3.0.30729; .NET4.0C; BRI/2)
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; Win64; x64; Trident/5.0)
Mozilla/5.0 (Macintosh; Intel Mac OS X 10.6; rv:11.0) Gecko/20100101 Firefox/11.0
Mozilla/5.0 (Macintosh; U; Intel Mac OS X 10_4_11; en) AppleWebKit/533.19.4 (KHTML, like Gecko) Version/4.1.3 Safari/533.19.4
Mozilla/5.0 (Windows NT 5.1; rv:11.0) Gecko/20100101 Firefox/11.0
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; WOW64; Trident/5.0; FunWebProducts)
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; WOW64; Trident/5.0; yie9)
Mozilla/5.0 (Windows NT 6.1; WOW64; rv:11.0) Gecko/20100101 Firefox/11.0
Mozilla/5.0 (Macintosh; Intel Mac OS X 10_5_8) AppleWebKit/534.50.2 (KHTML, like Gecko) Version/5.0.6 Safari/533.22.3
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.0; WOW64; Trident/5.0)
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.0; Trident/5.0)
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; Trident/5.0)
Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; WOW64; Trident/5.0)


The interesting bit is that the significant amount of these (when we strip out Chrome) are MSIE on a Win7 base, which makes me inclined to suspect something funny with Win 7, but there's at least 2 instances of OS X in there, and 2 instances (FF 10.0.02 and FF 11) on NT 5.1 (XP base)

If we throw out the OS X and XP ones as outliers due to something else (people monkeying with settings, who knows), that leaves us with a pretty clear indication that -something- in Win 7 has got some kind of naughty behavior with SSL, but I'll be damned if I can come up with anything. I spent half of last night trawling google for Win 7+SSL issues and just didn't find anything of relevance.