s3c tipped us to an infrared remote extender at Electronics Lab. A 555 timer IC is set to oscillate at 38kHz. Each IR pulse from a remote control, detected by a TSOP1738 IR receiver module, activates the timer. The timer blinks several IR LEDs through a transistor at 38kHz, recreating the input signal. Handy little device with no programming required.
Thanks for the tip!