DMX512 standard is based on RS-485.
At the data rate used at DMX512 system (250 kbps) the communications should work well up to distances of 4000ft (a little bit more than one kilometer).
The theoretical length limit of a DMX512 cable (from source to final terminator) is 1KM, about 3280 feet. However to work reliably at this distance you must have perfect source, termination, and cable of adequate cross section. Being pragmatic, it's best not to run a show at the limit of technology, and choose a smaller 'maximum' for your own peace of mind, say 1500 feet.