I've had exactly the same problem with my 1986 Cherokee. What is happening is that the vacuum motor on the axle isn't disengaging the axles from the differential. Simply replace the vacuum motor with a new one and the problem will go away.
On the Cherokee, instead of freewheeling hubs, the right hand side axle is split with two splined sections. Normal 2WD operation the spline joiner is slid on to one axle section. The spider gears in the differential rotate in opposite directions and the differential center section is stationary. When placed in 4WD, the spline joiner slides to connect the two splined axle sections thereby locking up the axle. There are three hoses, one to engage the axle via the vacuum motor, the second to disengage the axle via the vacuum motor, and the third to send the "I'm locked up" message to the light on the dashboard.
Walt Johnson.