Time Machine stuck at "preparing backup"

A few days ago I noticed that Time Machine had stopped backing up. I discovered that my external disc drive was no longer showing as connected to my iMac. I did a quick reboot by physically disconnecting the external hard drive — a WD Passport for Mac — then reconnecting to the USB port, which seemed to fix the problem. Except that since then every morning when I reboot from a cold start I have to reconnect the external disc. Time Machine has begun sticking at the "preparing backup" stage and is not backing up. I'm wondering what's going on and if the problem is with Time Machine or with the external disc. I've run a diagnostic on the external disc with both Disc Utilities and the WD Drive Utilities application, but nothing bad is showing. Any thoughts? I'm still using the Catalina operating system version 10.15.7.