Driving 3ft (long) ribbon cable from an IC
You should get a scope on the lines to see what is going on when the cable is connected. If the drivers are "giving up" as you say there is a very good possibility that they are being fried by under voltage or over voltage spikes due to reflections coming back down the cable. The scope can help to identify if this is happening.

Voltage spikes that go over the driver VCC by much more than 0.3V or lower the the driver GND by -0.3V can cause latchup or permanent damage to the driver. If the driver is experiencing latchup you may be able to turn off all power and let the board sit over night. It may work again after the trapped charge in the chip that kept the stray PNPN junction in the chip biased has a chance to bleed away.

One of the simplest solutions to this problem is to place small value resistors in series with the output pins of the driver. Select the resistor size such that the resistor value plus the output impedance of the driver begins to match the cable characteristic impedance.

You may want to also look at selecting a driver/level translator chip built with a slower process technology to slow down the rise and fall times of the driver outputs. This will go a long way toward helping to reduce the amount of potential +/- overshoot seen in the cable.