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I have about 3000 items in my kindle DX which includes about 300 collections.
My Kindle has become sluggish and even freezes at random times.
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Actually, I'd be rather amazed if it
didn't have some performance issues.
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I am guessing that maybe I have exceeded a limit of the Kindle but I can not find any information about that.
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It's the "Fill a device up and it won't run nearly as well as it did empty" rule.

I'm sure if you did a factory reset and started over with a more reasonable sized library, it would return to working normally. Just because you
can put 3000 items on the Kindle does not mean it's a good idea to do so.