time stamp not working

Also, have you tried resetting your phone modem?

iT IS A vTECH MODEL is 81212. Put in new batteries, followed instruction in manuel to set. Where would phone modem be- is it my actual modem? The call log looks like time is correct.

It depends, you might use your phone modem for internet or you might use a different modem/gateway. It would be what ever device you have with a phone cord(RJ11) coming out of it. Try entering 192.168.100.1 in a browser. If nothing comes up you either have a phone/internet/wifi combo(AKA gateway) or a separate phone modem not connect to your network. If a gateway, try 192.168.0.1. I can give better instructions once I know what you have.

You can log in to your Cox account to reset devices.

Time on handset is set on the PHONE, not from the modem. Refer to www.google.com/url

I set it per the instructions

time of day on my handset

Still would not have anything to do with the modem or the Cox service, as it doesn't supply Time Of Day, it supplies voice from another person. TOD functions on your handset is a function of your handset, or base. 

It seems this has happened before. See thread here. A reset helped some.

Could just be weak batteries.  Both were installed at the same time, so both are dying at the same rate.

I read that thread. That is my situation as well. Do I just unplug my modem to reset it?

Another thing I might suggest is logging into the phone modem and see if the UI has a date/time section and if it's correct. I seem to remember the DPQ3212 having it but not sure about the TM3402.