Matt's comments are (as usual) very good.
One other possibility might be that the starter contacts in your ignition switch are
fragmenting or sticking, however disconnecting the small wire from the solenoid should
show if that is the problem.
Although a 122 will usually work very well with a surprisingly weak battery, sometimes
they will do some pretty strange stuff! Therefore a good charge is always good.
--
George Downs Bartlesville, Oklahoma