DNS or DHCP update problem

i make a dialup over the telephone between 2 diferent pc's both of them are
windows server 2003, one of them is part of a domain with DHCP server.
the problem is when the 1st pc dials the pc that is connected to the domain,
normaly an IP will be assigned to this pc, for exemple : 192.168.16.223, so
when i ping the server name the result will be normaly:
reply from 192.168.16.223: bytes=32 time=150ms TTL=128
now if i intialise a dialup again, the pc will be assigned to a diferent IP
for exemple: 192.168.16.222,
but if i ping the pc name, it will try to ping the old IP that does not
exist anymore and the result will be:

pinging pcname [192.168.16.223] with 32 bytes of data:
Request Timed Out.

so i donno what is the problem, it's like the DNS is not updating the name
of the pc.
how can i solve that? it's very important to me to ping the name and get a
reply, cause i make an SQL synchornization between those 2 pcs

waiting for ur reply
thanks in advance
Sensay.