This is the classic collision between an old application and modern Windows security, since Eudora predates the permission model newer Windows enforces and the error is Eudora being blocked from writing to the registry areas it expects, so the fixes:

The permissions cause and the run as administrator fix, the first thing to try: newer Windows restricts which registry areas a program can write, and Eudora, written for an era without those restrictions, gets blocked writing its settings to the registry, producing this error. Running Eudora as administrator often resolves it, right click the Eudora shortcut, Run as administrator or set it permanently in the shortcut's Properties, Compatibility, Run this program as an administrator, which gives Eudora the administrator permission its registry writes need.

The compatibility mode addition: alongside running as administrator, setting compatibility mode for an older Windows version, in the same Compatibility tab, Run this program in compatibility mode for an earlier Windows, helps Eudora behave as it expects on modern Windows, the pair of compatibility mode plus administrator being the standard treatment for old applications hitting modern permission walls.

The registry permissions route, for a persistent case: if running as administrator does not fully resolve it, the specific registry key Eudora writes to may have permissions that even an administrator run does not satisfy, addressed by granting your user account full control on Eudora's registry key in regedit, under HKEY_CURRENT_USER or HKEY_LOCAL_MACHINE Software Qualcomm Eudora, though this is more involved and warrants care and a registry backup before editing.

The bigger picture given Eudora's age: this error is a symptom of running a long discontinued application on an operating system built well after it, and while the administrator and compatibility fixes work, the recurring friction is Eudora simply being from another era. The compatibility approach keeps it running for now, and the mbox files Eudora stores its mail in remain directly importable into modern clients whenever the accumulating friction makes moving off Eudora worthwhile, the same portability that makes the eventual migration straightforward, worth keeping in mind as these era errors multiply.