Every time I restart my PC I am asked to sign back into LR!

Sign out of both existing devices.

I also get this same problem occasionally, but only on my PC which  tells me I am signed in on  "John's PC" and "John's Mac" and that I have reached the 2 computer limit, despite being on "John's PC". You seem to have got two instances of the same Windows machine.

I've tried to get Adobe to look at this, but it seems to slip between the Lightroom and the Adobe's CC authorisation teams. I think it's the latter, but I've not been able to make progress.

Uninstalling or cleaning the Adobe CC installation does no good.

So just sign out of both devices, and as you know you can continue until the next time.

P.S. Something to inquire about just in case

On a daily normal basis, if you bring up your Adobe Creative Cloud Desktop App, are you signed in

and as such, when you bring up that Adobe Creative Cloud Desktop App, you are not presented with the sign in dialog?

Amongst the several things that signing in accomplishes (following not entirety of what occurs) is

• authenticating your account, your plans, your payments
• checking activated devices
• and if that passes mustard, activating your apps on the computer

Sign in and sign out to activate or deactivate Creative Cloud apps

One big issue that occurs if you sign out is  as follows:

• deactivates apps on your computer

Now, if you are signing out, then the question is why?

Note that lack of Internet connectivity, if you were previously signed in, and did not sign out, will not effect the Adobe Creative Cloud Desktop App in terms of it thinking you are signed in.

If the Adobe Creative Cloud Desktop App is getting signed out without your action, then something is wrong.

Creative Cloud signs you out or asks you to sign in repeatedly | 2019 and later versions

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A related inquiry

Some old users have a habit of signing out of the LrC, the individual app. This may come from way way back when. It is not required. It is not advisable.

My post is withdrawn.

Sounds like you need to bring up Adobe.com, and inspect what devices you have activated.

Following is not the only way to accomplish that.

1. Go to adobe.com. You may or may not be signed in, sign in if you are not:

2. Click on your account button

3. Select manage account

4. Under the Plans and payments tab, select Activated devices

 5. Look at what is activated, perhaps one is old and no longer used. Deactivate any as you see fit

 6. Note that when you launch the Adobe Creative Cloud Desktop App, on your computer, and sign in, your computer should get added to that activation list. (as long as the 2 computer limit is not hit)

Followup

An alternative to starting at adobe.com, is to bring up your copy of the Adobe Creative Cloud desktop App, and click on Manage Account:

The problem seems to be that that 'Dads-PC' is seen as two different computers for some reason, and so your computer (is that also 'Dads-PC?) is seen as the third one that tries to use Lightroom, which is not allowed. https://helpx.adobe.com/manage-account/kb/troubleshoot-creative-cloud-sign-out-sign-in.html

Hi , I've moved your post from the Photoshop forum to the Lightroom Classic forum where you are more likely to get help with your issue.

Dave