How can I stop my Xbox One from continually signing me out?

Possible solutions:

1) Just like GamerM said if you are afraid you got hacked please reset your password and enable 2FA (Two Factor Authentication) so it does not happen gain.

2) Check your network, double check NAT is open, try rebooting your modem and router.

If that does not help:

1) You can go ahead and delete your profile of your xbox one and redownload it:

1. Go to Settings, and then select System.
2. Select Storage.
3. Select All Devices.
4. Select Gamer Profiles.
5. Select the gamertag that you want to delete.
6. Select Delete.
7. Select one of the following:
8. Select Delete Profile Only. This deletes the profile but leaves saved games and achievements

2) Clear your Xbox One Cache:

1. Turn off your Xbox One.

2. Once the indicator lights on the front of the Xbox One and the console's power brick are off, unplug the power brick from the back of your console.

3. Wait at least 30 seconds.

4. Plug the power brick back into your Xbox One and turn it on.

3) Recover your Xbox profile:

1. Press the Xbox Guide button on your controller (large X button in the center of your controller).

2. Select Download Profile.

If you're not seeing Download Profile, press X to sign out of your profile.

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Sources: Microsoft Answers and Good Old Activation Support

This is possibly due to an issue I personally experienced where I was always getting signed out. I also had an external hdd. I noticed the light wasn't on and I touched the cord. Light came on and it immediately signed in with no further issues. Hope this helps.