It may depend on to whom the letter was sent. It may have been routed to a different department or manager depending on the complaint itself and make take longer to get a response.
If it was a complaint about an event at a resort, it may have been referred to the general manager for that resort. In most cases, it's much better to direct any complaints to the highest level while you are there instead of waiting until after you return. That way the resort has an opportunity to try to correct the issue at the time and/or contact all parties who may have played a role in the issue. After the fact complaints do take a lot longer to track down.
Good luck!