Why would a 1993 Mitsubishi Eclipse automatic tranny work fine for about 5 or 6 miles then when stopped stay in second and not shift to low or drive until you take the battery cable off ane put back?

The TCU (Tranaxle control unit) puts the car into limp mode. Might be the TCU, but more likely than not, it is a transmission problem. Removing power from the TCU erases the memory, until it sees the fault again and puts the car into limp mode.