I had problems with this for my flamingos in the beginning, but I found out it was because the keeper would only put feed in their enrichment feeder - my amount of flamingos would finish it off way before the keeper was on schedule to refill the feeders, resulting in several flamingos dying (a shame considering the CC "price" on flamingos).
I'm sure you already saw this, but give this a read, there's some great tips:
Hey all, thank you for your feedback regarding the Zookeepers and their tasks. We’ve been getting reports of Zookeepers not feeding animals and some starving to death. Here are some possible reasons: If your zookeeper is inspecting the habitat and then leaving without preparing food for the...
forums.frontier.co.uk
All my keepers are in work zones, and I have 1 specific work zone with 2 habitats (okapi and bongo) but just 1 keeper. It's been working problem free for several in-game years, so it is possible. In the end it's down the amount of animals in the habitat (more animals, more waste => more time spent cleaning, less time spent feeding) as well as distance from keeper hut to the feeder (not just the habitat gate, the keeper still needs to spend energy and time walking to and from the feeder)