There are a number of possible reasons:
1) Just having a foreign object in the mouth may stimulate excessive salivation (think of the trick of putting a pebble under your tongue when you're thirsty and don't have water to drink). If the mouthpiece fits badly, the problem could be worsened.
2) It could be that your wife is anxious and feels like she needs to grip the mouthpiece with her teeth, and therefore she chews her mouthpiece. This would make the salivary glands "think" that there's something in the mouth that needs to be washed down and swallowed, and of course, the mouthpiece can't be swallowed, so the salivation continues unabated.
3) The mouthpiece may have some chemical or rubbery taste to it that it stimulating the salivary glands to produce enough saliva to wash the taste away.
Depending on the cause, you can find some remedies for it. If it's a simple matter of getting used to having something (anything) in the mouth, have her watch tv or do other tasks while holding a mouthpiece in her mouth and the problem may just go away on its own. If it's a fit problem, get one of those moldable mouthpieces that you put in hot water and can trim down for a perfect fit. If it's anxiety, sometimes a different mouthpiece, like a comfo-bite type one that has a sort of upper-tooth bridge helps the diver feel like the thing won't just slip out of the mouth. If the mouthpiece tastes bad or has some chemical component that irritates your wife's mouth, try a different brand until you find one that doesn't provoke the reaction.
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