I'm having the same problem with 10.7.5 server. (two of them)
During the renewal I watched the Console and I think the SSL certificate of the Apple servers is no longer trusted.
(or the Server versions are to low)
Aug 15 10:23:08 login.********** servermgrd[23349]: Got connection error: Error Domain=NSURLErrorDomain Code=-1200 "An SSL error has occurred and a secure connection to the server cannot be made." UserInfo=0x7fb8f5aab9a0 {NSUnderlyingError=0x7fb8f15af450 "An SSL error has occurred and a secure connection to the server cannot be made.", NSErrorFailingURLStringKey=https://identity.apple.com/pushcert/caservice/renew, NSErrorFailingURLKey=https://identity.apple.com/pushcert/caservice/renew, NSLocalizedRecoverySuggestion=Would you like to connect to the server anyway?, NSLocalizedDescription=An SSL error has occurred and a secure connection to the server cannot be made.}
Aug 15 10:23:08 login.********** servermgrd[23349]: Request for push certificate failed: reason = Local, error code = -1200, error = Error Domain=NSURLErrorDomain Code=-1200 "An SSL error has occurred and a secure connection to the server cannot be made." UserInfo=0x7fb8f5aab9a0 {NSUnderlyingError=0x7fb8f15af450 "An SSL error has occurred and a secure connection to the server cannot be made.", NSErrorFailingURLStringKey=https://identity.apple.com/pushcert/caservice/renew, NSErrorFailingURLKey=https://identity.apple.com/pushcert/caservice/renew, NSLocalizedRecoverySuggestion=Would you like to connect to the server anyway?, NSLocalizedDescription=An SSL error has occurred and a secure connection to the server cannot be made.}
So not yet an idea, but hopefully with these console outputs we get somewhere?