After logging into the WHMCS, making any changes or modifications may log you out.
By default, WHMCS has a security setting that should help prevent cooke/session hijacking. However, depending on your device or network configuration, particularly if you have a dynamic IP address, it may cause WHMCS to detect normal actions as false positives. In turn, this causes the WHMCS software to log you out.
If you have a dynamic IP address or similar network configuration that triggers this feature to log you out, you can simply disable it under:
WHMCS >> Configuration >> System Settings >> Security Tab.
Disable Session IP Check
This is used to protect against cookie/session hijacking and ideally should remain unticked. However it can cause problems for users with dynamic IPs or using mobile devices (iPhones etc) so can be disabled by ticking the checkbox.
More details available in WHMCS's official documentation.