Do you have the solid state flasher system? If so there are a couple of possibilities.
The flasher will stop flashing when it gets too hot. When this happens the end is near for the flasher unit.
The flasher will also just stay on solid if there is a short in one of the 4 wires that it feeds. Common spots are places in the harness where those little metal frame clips secure the harness to the frame. There was a modification to the M151A2 Jeeps to prevent flasher failure the short would cause by installing a fuse on the power in wire (460/461).
The solid state flashers are kind of pricey. They can easily be replaced with a normal 2 prong flasher (in 24 volt of course) if need be.
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