My guess is a dirty "ignition" switch that makes unreliable contact. Your model uses a stop solenoid with two coils: "pull-in" and "hold." The low-current "hold" keeps the solenoid engaged after a brief high-current pulse to the "pull-in" coil. You must be getting the "pull-in" pulse or it would never start. So the current to the hold coil is suspect and the key switch (and fuse, connectors,and wires) is the only thing in that circuit. Also, intermittent function of this switch is commonly reported on TBN. There are unconfirmed reports of a new switch design but it may not be improved. A new switch is about $100. Several owners reported success after spraying WD40 in the key hole. Others have disassembled, cleaned, and lubed their switches, which fixed the problem. If you decide to disassemble your switch, take a photo or two during dis-assembly (to record orientation of things) and be careful not to lose any parts. The electrical part of the switch is very simple: it's a copper disk with raised areas that wipe the various contacts as the key is turned. But there are springs and ball bearings to maintain pressure on the contacts, return from "start", and create the detents.
By the way, another possibility is losing glow plug current when the switch returns to "run", also caused by an intermittent key switch.
