Upon a quote revision not only all items are re-calculated but also inputs are re-generated (by running them once in the syntax check mode; the same way as it is done when adding a product).

When inputs with the same name are generated, the values are carried over from the old version. Inputs that do not exist anymore are discarded and new inputs are added. The reason why this is done is that the formula or other things may have changed between the versions. Hence you need to do a full "at the current time" sanity check, otherwise you would carry on with an old format that may be outdated already.

When you have inputs in the header formula, it becomes tricky. As described above, the input generation is on the item level and drops all non-generated inputs as it considers them outdated.

 The conclusion is that ideally the line item logic should create these inputs. Then they will stay.

Example

for (lineItemMap in quoteProcessor.getQuoteView().lineItems) {
    if (lineItemMap.folder) continue  //skip folders
    
    quoteProcessor.addOrUpdateInput(lineItemMap.lineId,
            ["name"     : "SampleInput",
             "type"     : InputType.STRINGUSERENTRY,
             "required" : true
            ]
    )
}

api.stringUserEntry("SampleInput")