If it happens after the LM293 gets hot, then it would be safe to assume that you have a problem caused by heat. When the device gets hot the characteristics of the internal transistors change and they don't switch on and off cleanly. Or they might even try to stay on. You are drawing too much current.
The datasheet shows two different versions, I think, can you measure the windings' resistance to see if its 5.5 ohms or 30 ohms?Also what voltage are you using?