Noah the donkey fell into the 7ft (2m) ditch in Heydon, Cambridgeshire, on 17 August and was freed by firefighters.
Elaine Fisher who runs the stable where he is kept said the cover was taken some time during the previous weekend.
The donkey is still being treated at an equine hospital.
Cambridgeshire fire service, stable workers, a vet, and a man with a mechanical digger worked into the night to save Noah, holding his head above the water.
Stable worker Edward Stanford said: "The cover was there on the Friday when I was working in the field, then obviously by Monday it had gone.
"Whoever stole the drain cover obviously didn't think of the consequences, or perhaps they just didn't care."
After he was winched out, it was initially thought Noah had suffered just scrapes and bruises, however, on Thursday Mrs Fisher said he "went into shock as donkeys get very stressed".
Noah was admitted to Cambridge University's equine hospital where he is expected to remain for several days.
"It was touch and go over the weekend but he seems a little better today," said Mrs Fisher, who runs Lovely View Stables.
A Just Giving page has been started to help fund Noah's care. So far about 40 people have pledged more than Â£700 and many are following Noah's progress on a Facebook page.
Noah is owned by All Saints' Church in Melbourn, which is holding collections to help with the bills.
The donkey is well-loved in the village having starred in the church's Nativity services for the past five years.
A donkey that was at the centre of a five-hour rescue after falling into a water-filled storm drain ended up there because metal thieves stole the cover from his field, a stable owner said.