If this is an IMAP mail account, it may be that your email service provider has a storage limit for your account and that you have reached it. if so, you could - move to a service provider which offers unlimited storage, or - pay for additional storage if your provider offers it, or - move some emails from your inbox to a folder you create in the 'Local Folders' account on your machine. They are then stored on your own computer, not on your provider's server, and you can store as many as you have capacity for. But remember that you should keep backup copies for when you replace your present computer: keeping them 'forever' is a long time!

I have 2 computers. House and work. The comp at the house has the same Mozilla and it does not have this problem. The comp at work recently crashed and had to re install and software and since the re install it has been deleting emails in the INBOX that are more than 15 days old. I checked with my server. The amount of emails are not held at the server. They are deleted after download.