Mammalian expression constructs for certain genes such as human c-KIT are notorious for undergoing frequent recombinations during cloning and transformation steps in molecular biology labs. Experts suggest that certain genes are “toxic” to bacteria thus leading to a situation in which recombined plasmids are favored. While the molecular mechanisms for this toxicity may be unclear, the end result is that efforts to amplify, subclone, mutate, or make derivative vectors often result in a new plasmid with unwanted sequence errors.

Source: http://en.wikipedia.org/wiki/Agar_plate
Online science discussion forums such as ResearchGate include a variety of strategies proposed by researchers experiencing this kind of plasmid instability. Suggestions include advice such as culturing the bacteria at room temperature rather than 37°C, culturing on plates rather than in flasks, using low copy number EPI400 competent cells, picking the small colonies rather then the large ones from the LB plate, replacing the ampicillin resistance cassette to prevent satellite colonies (so you can see the small colonies), or using a Gateway vector.
But which methods work best?