I have a 5C and it will not keep the correct time. I have done a soft reboot, set it manually and nothing works

I have seen this before and it is generally a hardware issue. Make a backup of your device and then restore the device as new. Do not add any content to the device and then either set the time automatically, or manually and test for a short period of time. If the time slows, then make an appointment at the Genius Bar of the nearest Apple Store or Authorized Apple Service Provider to have the phone examined.

You're welcome.

If restoring your device doesn't work, it could be a carrier issue. I do technical support with a major wireless carrier and I've seen situations where the issue is sometimes a network issue with your carrier. If a restore doesn't work, try contacting your carrier and see if there are any other reported issues. Your carrier has the ability to open network trouble tickets and can determine if it's a network issue. Sometimes it can take a few days for them to work a ticket, however it's better to wait to find out if it's a network issue before you run out and get a replacement device because you could be potentially facing the same issue on the new device if it has nothing to do with your software on your phone.

While the network could affect the device if the time setting is on Automatic, it would not affect the device if the user is setting time manually. I agree that it can happen on the automatic, especially since the time can come differently from individual towers, but the OP stated they had set the time to manual and was still experiencing the problem.

Regardless if the time settings are set to manual or automatic, an updated carrier settings push can change the time settings on a phone whether or not it's been preconfigured by the user or if it's being automatically configured by the network. We open network tickets all the time where I work that deal with this exact issue and there have been many occasions that it happens to be the network that's causing the issue because it's consistently sending a carrier update to the device due to the device not registering that it's fully established on the network due to possible roaming from their home area, or somehow the device is out of range or not properly communicating with the MSC.

Sometimes it's a software issue and a restore will fix it, and sometimes it's a third party application that's causing the device to revert back.

There are many different factors that play into something like this, that it's hard to just immediately assume it's one specific piece of hardware, or software or network push. Just say for instance it's nothing wrong with the phone, but something wrong with software on the device, or something that's being caused by a third party application or maybe a network issue ...

The user reaches out to Apple, gets a new phone, loads everything back onto the device and the issue happens again...

Right back to square one.

It's important to completely troubleshoot all aspects that could be affecting the device, not just randomly assume something is wrong with one specific part of the device and immediately refer them to someone for a replacement. Sometimes, a replacement device can turn out worse than the actual device having the issue.

And that is why I recommended restoring the device as new and test without any additional content being added back to the device. I did not advocate not troubleshooting the device, nor did I immediately refer them to a replacement. I can appreciate your post, but please do not assume that I do not know what I am talking about. That is not how the forum works. As I indicated, I have witnessed this type of behavior and participated with other users experiencing this issue.