I worked through this very problem only yesterday!
It's a permission problem. Standard Windows Users (without Administrative permissions have this problem) - but there is an easy solution 😀.
When you do the Certificate Enrolment on the client machine, it actually tries to install two certificates not one - but you have no visibility of this...
The user's specific certificate with its private key can be enrolled into the the User's Personal Certificate Store in Windows (with standard user permissions) without any problem, but the corresponding Issuing Certificate from your Firewall Manager also needs to be located in the Trusted Root Certification Authorities Store on your computer. The certificate enrolment process tries to install the certificate if it doesn't exist, but the process fails if you don't have Administrative permissions on the computer.
The solution is to use Group Policy to pre-distribute the Issuing Certificate to the Trusted Root Certification Authorities Store on all the relevant computers in your domain (for example all your laptop computers):
Required GPO settings:

When you create the GPO, you just need a copy of the required certificate (you can copy it from an already working computer in .cer format). The certificate becomes embedded as part of the GPO object.
After the computers refresh Group Policy, they now have the required certificate located in Trusted Root Certification Authorities Store. Because the valid certificate is now already located on the computer, when you perform certificate enrolment process, it will now work without error.