It will take a little longer since you mailed the renewal in. If done by phone you'd be looking at about a two week (or less) turnaround. By mail, you have to add at least another week for your letter to get there, be opened and routed to the right area, then processed.
Disney will tell you to allow 30 days but that's mostly legalese to cover themselves. If you don't have it within 30 days, call. That means there's a problem somewhere.