Sounds like you are still having something of a problem.
I think it would help to distinguish for you the connection from the the LU to LU sessions.
The connection is what, as I read your description, goes into "Pending" Status. CICS does not service the connection, the VTAM PU on the mainframe to which you physically connect is the mainframe component to which the connection talks. CICS to you is an LU, not a PU.
To put it differently, a "connection" is actually VTAM on the mainframe talkiing to HIS, with HIS playing the role of an emulated 3274 (slight modifications to the above apply if there are LUs with LOCAD = 0 on the VTAM PU to which you talk = but these modifications, for the most part, do not affect the connection's ability to go "active".
So, if you are having problems, they can be of two basic varieties:
(1) The VTAM PU to which HIS talks fails to recognize that the HIS emulated 3274 is attempting a reset operation (that's what stopping and starting the connection is supposed to do). In many cases the VTAM PU in fact will fail to recognize that the HIS emulated 3274 has logically dropped the connection.
(2) An error on the HIS side results in an invalid notification to VTAM, so VTAM never knows HIS is trying to reset the connection.
OK, how do you know which it is, and what do you do?? Which was, essentially, your original question.
When the connection drops, call the VTAM sysprog on the mainframe end and ask him to use NETVIEW or the equivalent to look at the PU to which you connect. If the PU still shows you in session, ask the sysprog to send you the VTAM definition for your PUs and the LUs that you own on that PU. Look for settings that are inconsistent with HIS.
If the PU knows you have dropped the connection, then the problem is likely in HIS or on your network. You don't say if it is 802.2, SDLC or whatever. It makes a difference.
As goes without saying, make sure your HIS is Service Pak 1.
Hope this helps.