I am using g.723.1 and do not have such problem.
CODEC is not reason for this problem.
You must know or Cisco must know which CODEC they should use
g.723.1ar
g.729br8
or….
What exactly is “disconnection rate is high”.???
Do you have low traffic from your Cisco partner or what is it?
Does the Cisco sending in e.164 format (H.323 does specify the difference between a public and a private number)