If adding the terminating resistor causes the link to drop, assuming the terminating resistor is connected correctly, that suggests that the bus is loaded to the point where it's only marginal functional anyway. Are there perhaps extra terminating resistors connected? Perhaps when it was wired as a start someone had put a termination resistor at the end of each arm?
You might try measuring the resistance between the A/B terminals with no driving device connected (possibly with all of the devices off if that can be arranged), if it reads ~120R then it's terminated properly at one end, if it reads ~60R then it's properly terminated at both ends. If it reads lower with everything powered off then it may be biased somewhere or you might have an extra termination. You can also measure the DC voltage on the bus when it's driven to a known state, and note what happens when the termination resistor is connected.