Large input context models are gpt-5.4+, with 1050000 context window possible.
GPT-5.x models prior are a 400,000 context window, of which 272k can be sent as input, with the 125k remaining reserved as output context generation.
Sending more than 272k tokens to a large context model will trigger double-the-price, somewhat “turning on” long context mode.
What you show and experience should not be the case, but instead would be a bug: the model’s “short” total context window is not a maximum 272000, but instead 400k as before. All gpt-5 models state a 128k output, from which the input shall not consume, but should be reserved for generating an output for you.
“Long context” vs you running “Short context” on an input under the high-price switch shall not be an off switch of output of only 272k total context window if you do not trigger it with a large input. It shall perform like gpt-5.2 across all models, always providing you output space.
What you could try: sending the API parameter max_output_tokens, and setting it much higher than you might expect. This is the total budget for an API call’s output, which not only includes reasoning tokens, but also when internal tools are used, collects all generated tokens into a final report.
Then if running up against a bug with new models gpt-5.5 or gpt-5.6, you could complete the $1.36 call there against gpt-5.2, a cheaper input price that has no alternate “long” mode that might have been provisioned incorrectly.
Also: watch and collect the entire API response object: any refusal or error output items, status “completed” or not, or the report in the field “incomplete_details”. That may give a bigger picture of what is terminating the output before a seen response.