It splits because emulsions are fragile
Hollandaise is an emulsion: egg yolk holds melted butter together with lemon juice and water. It works because lecithin in the yolk wraps each droplet of butter and keeps it suspended in the watery part. It fails because that suspension is delicate. Add the butter too fast, change the temperature too quickly or stop whisking, and it collapses. The fat separates out and the sauce splits.
So take your time and watch the heat. Add the butter in a slow stream, not in glugs. Keep the bowl at a steady 60 to 70 degrees Celsius, warm enough to keep the butter liquid and cool enough not to scramble the yolk. Whisk constantly. If the cook can't get three uninterrupted minutes to make a fresh batch, the sauce will fail.
It scrambles when the heat creeps up
The most common reason hollandaise fails is heat creep. The cook starts the sauce at the right temperature, gets called to the pass to plate something, comes back, and the bowl has crept past 80 degrees. The yolks scramble and the sauce goes grainy and broken. No amount of whisking will bring it back.
Take the bowl off the heat as soon as the sauce coats the back of a spoon. Hold it warm in a separate container, away from direct heat. If you use the blender method, the hot butter goes in below 80 degrees. The cook should be in charge of the heat, not the other way round.
It dies under the heat lamp
Leave hollandaise sitting untouched in a warming station for an hour and it stops being hollandaise. The fat separates, a skin forms on top and the lemon goes dull. By the time it hits the plate it's yellow paste under a layer of clarified butter, with a slight off taste the customer can't quite name.
Rotate it. Hold the sauce at 60 degrees Celsius or above in a covered warming station. Whisk it gently every 15 to 20 minutes to keep the emulsion together. Replace the whole batch every four hours. Even setting food safety aside, hollandaise older than four hours isn't the same sauce.
The four hour refresh is about flavour as well as food safety. That's roughly when hollandaise stops tasting like hollandaise: the lemon dulls, the butter goes flat and the texture coarsens. A customer ordering at 10:00 and one ordering at 14:00 should get the same sauce, and regular refreshes are the only way to make that happen.
It grows bacteria when it is held wrong
Hollandaise is raw egg yolk and warm butter, which is close to an ideal recipe for growing bacteria at room temperature. The FSANZ food safety rule is simple: hold it at 60 degrees Celsius or above the whole time, or chill it to 5 degrees Celsius or below and reheat it quickly to 60 degrees or above before serving. Anything in between is the temperature danger zone, and that includes hollandaise left on the bench during a quiet moment at 11:00.
That's why many serious cafes no longer use from scratch hollandaise as their everyday sauce. Making it isn't the hard part. Holding it safely through a six hour brunch service is, and a busy cafe kitchen often can't keep that up.
What serious cafes do
Many of the most consistent eggs benedicts in Australia are not made with hollandaise from scratch. They are made with a high quality prepared hollandaise from a serious supplier, held at 60 degrees or above, refreshed every four hours, and finished at the pass with a quick whisk and a squeeze of fresh lemon to brighten it up again.
Some kitchens call that heresy. Others call it common sense. From scratch hollandaise makes sense in fine dining, where the sauce is made for one table at a time and someone's whole job is keeping it alive. In a cafe doing 200 covers between 08:00 and 11:00, the best sauce is one the customer can't tell from house made and the kitchen can get right on all 200 plates.
If your cafe is committed to from scratch, set up the kitchen to support it: a dedicated cook, a dedicated bain marie, a refresh every four hours, a timer on the pass, no exceptions. If that isn't realistic for your venue, prepared hollandaise is the honest choice, and the better one for the customer.
In the end the hollandaise problem is about the gap between what a kitchen wants to do and what it can reliably do when service is flat out. Close that gap honestly and customers come back for your Eggs Benedict.