I would try taking his weekly amount of copywork and spread it out over five days (and not increase it no matter how tempting).
ETA: I meant to not increase it if you switch to five days. I'd split the longest line between two days before I'd increase the current amount of writing...for now, anyway.
If that's not feasible, I might reduce it from two lines to just one, making it a less tiring task, but one that is still done with consistency. There is lots of time to gradually increase the amount as he gets older.
Writing fatigue is an issue around here too. I don't give copywork but my son takes a correspondence course for French that has some writing in it. I always spread the pages that require writing full sentences over 2-3 days and give a page with matching or circling with it so the lessons still take about the same amount of time to complete and send in, but are more manageable for him.