I'm creating the first full backup on a new 3TB drive. Time reports just over 1TB will be needed. Drive returns a disconnect message and time machine stops after every 100-300mb.
My Mac runs High Sierra OS - 10.13.5
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Copying 100 MB should be pretty quick on a new drive with USB 3 and a Mac that supports it, so I would open the console application (use spotlight or find it in /Applications/Utilities) and sort messages on backup
If you see no messages, then you might need the command line tool tmutil status so find the terminal application and type the above characters in bold and report back / possibly in a new thread.
I'm guessing you can copy files to the drive and are not seeing an issue where the drive ejects and it's more about the backup stopping prematurely (or not even getting started).