The short answer is: This is the standard operating procedure for MVS and cannot be avoided.
The long answer follows:
The message "IEF352I ADDRESS SPACE UNAVAILABLE" is generated each and every time TCPaccess is shut down. This is an MVS system level informational message indicating that the ASID assigned to TCPaccess for this address space is now unavailable, and non-reusable for the life of the IPL. This is not a problem, and is standard operating procedure for MVS with applications such as TCPaccess that employ address space switching. TCPaccess employs address space switching as a means of providing services to other applications that need our services. As such, TCPaccess is required to make it's services available to all address spaces, since we do not know who will need to utilize our services. In order to make services available to all address spaces, IBM requires use of a system level linkage index. This system linkage index, or system LX, is associated with a table entry that is now connectable to all present and future address spaces.
It is IBM's design that ASIDs which are linked to system LX's are non-reusable for the life of an IPL after the address space terminates. There is no reason to worry about exhausting all available ASIDs provided MVS is configured with an active and dynamic environment in mind. One needs to ensure there are enough ASIDs available in the ASVT (address space vector table). There are three parameters in IEASYSxx that work together to establish the total number of ASIDs available:
MAXUSER, RSVSTRT, and RSVNONR
Of special note is RSVNONR. In the MVS Initialization and Tuning Reference, RSVNONR is said to specify "the number of entries in the address space vector table that are to be reserved for replacing entries that are marked non-reusable. A non-reusable address space is one where a job that ended had been running in a cross memory environment. When such a job ends, the system ends the address space and marks its associated ASVT entry non-reusable."
Furthermore, in the z/OS V1R5.0 MVS Extended Addressability Guide, 188.8.131.52 Using IEASYSxx to Avoid Running Out of ASIDs, IBM states, "you can reduce the possibility that the system will run out of ASIDs [by reserving] ASIDs through the RSVNONR and RSVSTRT parameters in the IEASYSxx member of SYS1.PARMLIB. The reserved ASIDs replace those lost due to cross memory activity."
Note that the sum of the values specified for the RSVSTRT, RSVNONR, and MAXUSER system parameters cannot exceed the maximum value as specified for the version and release of MVS running at a customer site. Also note, the default values for these parameters tend to be low, so one should refer to the MVS Initialization and Tuning Reference for more details.