Just to share....

If webmail failed to work after you switch IP to a different subnet, you'll need to update ZimbraMTAMyNetworks.

From ZimbraMtaMyNetworks - Zimbra :: Wiki

# su - zimbra
$ postconf mynetworks
mynetworks =

If mynetworks still point to the old subnet, you'll need to change it

# zmprov modifyServer zimbra.example.com zimbraMtaMyNetworks ''
# postfix reload
# postconf mynetworks
mynetworks =

then the webmail should work again...