Interference is unlikely to disrupt a signal powerful enough to drive a stepper, but the resistance of normal ribbon cable is a likely problem.
On the other hand, interference from the motor cable could disrupt other circuitry nearby, so some shielding might be called for.
Two experiments:
(1) run both steppers off short cables; they will probably work fine. (If not, give the "far" one its own driver amplifier)
(2) Run thick wire (cross section at least 1mm^2) to the far stepper motor to reduce the resistance in series with the motor. There's not a lot you can do about the extra inductance of the longer cable, but at low speed it's not likely to be such an important factor. This should give reliable operation up to a certain speed; but you may have to reduce the rate on this axis a little compared with the other axes.
The answer to the question you linked to explains that a 2.55V rated motor could work with the A4988 driver.
Answers continue on to explain the real constraint for a stepper is thermal, it could be 'cooked to death' by too much power.
The answers also explain the A4988 can be set to limit the current, so that a 2.55V stepper could be driven from a 8-35V power supply without damage.
The problem is trying to drive the A4988 with 5V, as Tut wrote, the A4988 minimum drive is 8V.
Looking at Allegro's web site for Bipolar Stepper Motor Drivers the A4980 is designed to operate at 3.3V or above.
I do not read Chinese, and I can not find any mention of the rated voltage of the stepper you linked to.
It looks like the motor could be made to turn at 5V. However getting that stepper to work reliably, with sufficient torque, at a high enough speed for your purpose, might be a problem at 5V.
I would try a higher voltage than 5V, maybe 8.4V of NiMh, as an experiment, using the A48988 drivers. (Edit: 7 x 1.2V NiMh is 8.4V not 8.6V corrected)
The current consumption of a motor is highly variable. In the absence of a datasheet, a reasonable guess is half-max speed is maximum efficiency, and happens around 1/2 maximum current.
One 0.45A motor might consume 0.225A if it is running at maximum efficiency, and so 8 hours would be 1.8Ah.
The maximum current is 0.45A, so one motor running at maximum current (and hence maximum power) would consume 8*0.45A = 3.6Ah.
Choose a battery, for each motor, in between those two.
The Remote Control model approach is to use LiPo batteries, which run at a nominal 7.4V (for 2 cells in series) or 11.1V for 3 cells in series. They are light, and can charge quickly. They need a LiPo charger, and they must never, ever be run too low.
(Have you access to any test equipment, for example a bench PSU which would let you 'dial in' the voltage and current?)
Best Answer
Start by checking the stepper coils for shorts. If the motors are of same type, all coils should have pretty much the same resistance. If one coil is shorted (or with very low resistance), for example, then this could possibly fry the driver as well.
Spec sheet says coils should be 1.25Ω, if it is less than that, that could be the problem.