Why is macmail deleting all inbox messages after a month?

I am using Mail 3.6 with Mac OSX version 10.5.8 on a Macbook. A few months ago, Macmail started deleting any messages in my inbox that were a month or more old. I've checked everything in Preferences and there seem to be no rules which are making this happen. I've checked with my email provider (Demon) and they say it isn't a problem at their end. Can anyone help?

Thanks!