Check under Settings-->date+time ...If there is an 'Set automatically' option set it to ON. If your Operator supports this feature, the time and date should get set automatically in a few of seconds of switching the device ON ..
I'm facing the same issue with my Lumia 800, or rather was. Here's my situation: initially the handset would keep resetting the date to 1980 (and a random time) each time I switched it off and on again. This happened whether I was connected to wifi/mobile data or not. I've recently done a reset of the handset (using the option from within Settings) and this has partially resolved the issue.
Now if I'm connected to wifi/data when I switch the phone off/on the date resets to August 2013. If, however, I'm not connected to wifi/mobile data when I switch the phone off/on the date/time remain unaffected. So this would suggest that it's not an internal battery issue which is what I first suspected. As it stands now then the best option is to reset the handset and then ensure you turn off wifi and data/internet before switching the handset off/on. Still annoying to say the least, but partial workaround.
Furthermore there is no automatic date/time setting to toggle on/off under the date/time settings (removed by the last update I gather?), just an option to toggle between 12hr or 24hr clock. My handset is on the latest OS version and firmware.
Any idea if Nokia/Windows are working on this issue? Just doing a Google serach for this issue and it appears that a fair few other Lumia 800 users are facing the same problem.
Update to my last post: the date time issue also manifests itself if the phone is switched off and on whilst being charged (whether or not it's connected to wifi/data connection).
Thanks for the advice. I tried reseting the phone after I backed it up to my PC. This solution did not work for me.
After a reset I went through the startup screens which includes setting the date and time. After this was completed I powered the phone off. When I powered it back on the date and time were incorrect again. I then did a restore from my PC and funnily enough when the phone came back on the date and time were correct. After a power off and on however they were incorrect again.
Can Nokia confirm that the Windows Phone 7.8 update will fix this? Otherwise I will try to get a refund.
One issue resulting from the time and date problem was with texting. The OS maintains a text message conversation that is ordered ny date and time. Once when I did not realise the date and time were incorrect I sent a text to someone and it did not seem to apear in the conversation stream. I retried several times until I realised that the messages were sent but with a much later date. I called the recipient and appologised for sending the same thing over and over. Now before sending a message I scroll the whole stream just in case.
The retailer has agreed to replace my handset. They said that they were not aware of this problem. Next week I will update on whether the new hardware has the same issue. Finders crossed.
I eventually contacted Tesco Mobile (from whom I purchased the handset) technical support and they offered to check the phone over for any faults. Anyhow, just had the handset back with a note saying that they couldn't identify or replicate the issue with the date time and that they had flashed the phone with the latest software anyway before sending it back to me. I've checked the software version and it's now showing Windows Phone 7.8! The date/time problem appears to have been resolved as well.
Will keep an eye on it though just in case it rears it head again....