The code is complex. Here is a set of proposed changes, for trunk:
1) remove PingInputStream. if rpcTimeout > 0 it just rethrows the exception. I expect that we always have a rpcTimeout. So we can remove the code.
2) remove the sendPing: instead, just close the connection if it's not used for a while, instead of trying to ping the server.
3) remove maxIddle time: to avoid the confusion if someone has overwritten the conf.
4) remove shouldCloseConnection: it was more or less synchronized with closeException. Having a single variable instead of two avoids the synchro
5) remove lastActivity: instead of trying to have an exact timeout, just kill the connection after some time. lastActivity could be set to wrong values if the server was slow to answer.
6) hopefully, a better management of the exception; we don't use the close exception of someone else as an input for another one. Same goes for interruption.
I may have something wrong in the code. I will review it myself again. Feedback welcome, especially on the ping removal: I hope I got all the use cases.