John Cockburn says:

Your problem could be caused by a variety of faults, for instance when did you last clean and oil the motor bearings. it could be a carbon buildup shorting in the commutator grooves, use a wooden cocktail stick to clean out the grooves or it could be the the brush’s worn right down and not making contact with commutator properly giving intermittent power to the armature. check all soldered joints (you did not say what manufacture the loco’s were made by so I am guessing Lionel for starters) having checked that the motor runs OK when power is supplied to the wires leading to the brushes if the motor runs continuously when power is supplied you need to look at the track and it’s connections if you have a test meter check each length of track to make sure that there is a continuous current supply, a rusty rail joiners, loose pin, broken wire or damaged soldered connection could be the problem.
Now check the height of the centre third rail and see if it has worn down, to do this turn off all electricity to the rails or you could end up with a short circuit, if you have a steel rule place it across the two running rails and see if there is a gap between the rule and centre third rail, if there is you will probably need to adjust the bar holding the rollers by slightly bending it down, hold the end of the bar nearest to the pivot pin and apply pressure at the roller end, this way you will not damage the pivot pin.
If the groove in the roller is very deep you may need to get a replacement set of rollers or you could make them yourself out of brass rod, obtain a piece as large a diameter as the rollers then find the centre of the rod and drill a hole the same size as the roller pin, if the roller is larger in diameter in the middle then the brass bar needs to be shaped in a lathe or in the chuck of a drill using a fine file being finished with fin emery paper, sometimes you can find spares on eBay but they can be quite expensive, I look for models that are being sold as spares or repairs making sure that all the parts are there that I want. Have you checked the controller, some controllers have a continuous winding round an insulated strip of mica or paxolene and contact is made when the arm fixed to the controller comes into contact with it and over time both items can become loose or worn down by continuous friction. I hope that you will find this list of tips helpful but it is by no means complete and perhaps someone else could take over where I have left off.
Kindest regards john.