There have been undocumented reports, agreements between experienced breeders that were never put to the test, never written in paper and to most of these breeders they really wished they never will be.
Cockatiels are relatively easy to breed. When a good pair starts breeding, one might have to intervene or they may never stop laying to the detriment of the hen's health. Per clutch you may find about four to seven or eight eggs but some might get discarded or destroyed before hatching or abandoned by the parents leaving only one or two to survive. Breeders believe this is a psychological instinctive trigger built in to the parent's system to provide better surviving results for the remaining chicks.
Now what are the triggers.
Food and Water
This is the most important trigger. Never let the dishes empty, there should always be an EXCESS of food. Like summer season in the wild, food is abundunt as seeds and fruits produces more than enough to support a big family. The parents upon seeing this will continue to provide for the chicks without the need to manage each meal. Once the parents notice that the food is scarce, (though you know you will provide it if need be) they will abandon the weakest, usually the smallest of the chicks and increase the survival rate of its siblings by reserving the meager available food for them.
Temperature and Humidity
Imitating the summer season would be the best approach, thus an indoor cage where temperature can be managed is a more appropriate location. Dampness of the nest box is a major factor for complete abandonment of the clutch. Provide proper cover from drafts, sudden temperature changes and rain if the cage is outdoors.
Pests/Predators
Make sure no pests like mites, ants and the like will enter the nestbox, precautionary steps should be taken before breeding, taking into account the sanitary steps for your nest site. If infested during the nesting process there is no other choice but to remove the parents temporarily, pull out the eggs/chicks and sanitize the site before returning them together.
Predators are common to an outdoor setup, make sure your perimeter is secure from cats, snakes etc. The railings of your cage can be more secure by doubling it up with chicken wires. Indoor setup is not devoid of predators. Inside, YOU are the predator. Do not startle the nesting family or it may destroy the clutch or abandon them completely. Cockatiels though are known to be one of the most tolerant pet birds during its breeding season just make sure you make slow, expected movements. When checking the nestbox it is customary to "knock" three times to let them know you are coming, this simple respectful act can save you lots of cheeky lives.