stepper issues

Thanks for all you help so far. I'm working with a high school
freshman to get a stepper motor to run a certain number of steps and
then stop - calibrate a small erector set car to run between 5 and 10
meters (we'll be told specific distance at the competition) and then stop.

We have combined 2 basic circuits to accomplish this task - a 555 as
monostable (adjustable time) dumping into a 555 astable to give steps
while monostable is saying "go" and the astable dumps into the trigger
of a 5804.

We get this circuit to drive a stacked can motor - we need like 30 to
45 seconds of run time. We don't have it hooked to the device yet -
the motor is just driving another free running gear. The motor starts
alright, but sometimes well into the run, it gets confused and
stalls/reverses.

A few notes about stuff we might have done wrong -
1 - we didn't use pullup/down resistors for the full, half, direction
pins - we just tied them to +5 or gnd.
2 - we hard wired this on an soldered experiment board and have wires
going everywhere. We initially did 3 circuits on 3 separate
breadboards and had the same problem. I thought it might be the
breadboards and the fact that we could only put about 7 V to the motor
circuit, but we get the same results with a wired cicuit all on 1
soldered breadboard and 9.6 V battery running the motors and dropped
down through a 7805 to run the 555's and 5804.
3 - we are limited to 9.6 V max by the rules
4 - we didn't use a PIC for a couple reasons - I wanted him to learn
about 555's, we didn't have PIC programmer in stock so I thought I'd
have him work on the 555 path while I researched and acquired
programmer - still hope to do this, but the competition that sparked
this project is Tues, Nov 20, so we are trying desparately to get this
circuit to work.

We'd sure appreciate your help in where to look.

Thanks again for your help so far, and for any you can give over the
next few hours/days.

Chuck