Ensuring HttpClient can be used safely as a singleton
Just a few things:


You have already named the variable _oneMinuteInSeconds - I'd say you don't gain much by initializing it via a TimeSpan the way you do it. Just saying _oneMinuteInSeconds = 60 would be good enough since it's quite clear what the 60 stands for.
Actually, according to MSDN the ConnectionLeaseTimeout is set in milliseconds as such your code is of by a factor of 1000 regarding the timeout (why the framework designers have not consistently used TimeSpan everywhere is a bit of a mystery to me).