Your results are going to a temporary file which disappears at EOJ.  Try
!file st=*st;old
(and the ;access=append is unnecessary, as >> means append.

!job SESCOUNT,manager.sys;pri=cs;outclass=,1;hipri
!purge st.pub.sys
!echo Session Counts for !HPSYSNAME,!HPDATEF    > st
!echo _______________________________________   >>st
!echo                                           >>st
!echo !hpsescount,!hpdatef,!hptimef             >>st
!save st
!eoj