Actionsupport in VF page and apex controller don't work properly

Hi everyone,

I'm developing a visualforce page with a couple of questions. Every question has a few possible answers, which I control with checkboxes(apex:inputCheckbox), and a text field(apex:inputText) next to the answer for additional information. I added an action support to the textfields, which controls the checkbox and changes the flag "isTextFIeldFulfilled". If a textfield is fulfilled then check the checkbox and set the flag to true, if not uncheck and set to false. I added also an outputText to debug the flag.The problem is that somehow the flag is not changed in the apex code, when the user writes something in the checkbox, but it's changed in the visualforce page.

Example:

I type something in the inputText, result: checkbox is checked and the outputText shows me that the flag is setted to true. When I call another function in the apex code later, the flag is false, although in the outputText it's shown as true.

Could someone tell me, what the problem is?

Thanks!