I too agree 
I am involved in two high priority cases for last two weeks or so.
We already have to battle time outs for desktops, putty AIX sessions and now for the OneSupport too.
But again if that is an idle connection to the back-end then I can understand as a DBA that it is still using some resources. And a watchdog process on SAP side may terminate it to release resources.
So if a middle ground can be found that will be great.
How about time out for "a business day" at least ?
Avinash