I have the exact same problem, 7031 event id's (7 over a 24 hour period) and several 5011 and 5009 event errors mainly related to the MSExchangeRpcProxyAppPool app pool.
I completely re-installed the system, and used recover server setup switch. Formatted the C drive and did not use the old MSexchange files (except for the mailbox database + log files).
This indeed leads to outlook being unable to connect, after a while (at the old system, anywhere between one and 7 days I couldn't even kill the process (access denied), the only thing I can do is a full reboot.
Now this is a Hyper-V VM, running on 2012, it runs the OS, Exchange 2013 CU1 (I didn't seem to have this problem when using 2013 RTM) and Remote Access and NPS.
Now I am not sure what else to do, as a complete re-install didn't seem to work at all.
edit:
After about 1.5 days, the server again needed to restart for outlook clients to be able to connect. (ActiveSync continues to work normally, so does OWA).
The RPC CA service failes, but a restart doesn't work as the old process is still running, no way to kill the old process, as any attempt either via taksmgr or process explorer leads to access denied (even after specifically assigning myself rights to the
process)
In event log, first 7031 appears, followed by 7032 and finally several 7011, and the 5011 continues to appear.
7031:
The Microsoft Exchange RPC Client Access service terminated unexpectedly. It has done this 1 time(s). The following corrective action will be taken in 5000 milliseconds: Restart the service.
7032:
The Service Control Manager tried to take a corrective action (Restart the service) after the unexpected termination of the Microsoft Exchange RPC Client Access service, but this action failed with the following error:
An instance of the service is already running.
7011
a timeout (30000 milliseconds) was reached while waiting for a transaction response from the MSExchangeRPC service.
and
5011
A process serving application pool 'MSExchangeRpcProxyAppPool' suffered a fatal communication error with the Windows Process Activation Service. The process id was '21368'. The data field contains the error number.