EDIT 8/10/2010: Please note that this blog post covers namely the history of named properties in Exchange. For updated and current guidance of how to deal with named properties issues, please see t...
Updated Jul 01, 2019
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Kevin, rather than a single explanation, I offer you a simpler way to answer the question.
Because your question was about named property quotas, I used the words "named", "property" and "quota" in a live search (use the search engine of your choice). I selected these words because I wanted to see what was already available about "named property quotas". I could also have inserted the event id but that would have taken more typing. Normally search engines rank things in terms of "relevance", so I selected the results from the top of the list, which is usally the most "relevant" ones. The first two are for a kb 820379. This KB relates to setting the quota, and by reading it, I found that it links to another kb, 898785, which describes one problem when this was exhausted. The good news is that I didn't even have to click that link - one paragraph below that link is a section that lists even MORE symptoms that could occur when the quota is reached. I'm sure if I had read the third or even the fourth result, I might have found even more information on what happens, but I leave that to you to explore.
Because your question was about named property quotas, I used the words "named", "property" and "quota" in a live search (use the search engine of your choice). I selected these words because I wanted to see what was already available about "named property quotas". I could also have inserted the event id but that would have taken more typing. Normally search engines rank things in terms of "relevance", so I selected the results from the top of the list, which is usally the most "relevant" ones. The first two are for a kb 820379. This KB relates to setting the quota, and by reading it, I found that it links to another kb, 898785, which describes one problem when this was exhausted. The good news is that I didn't even have to click that link - one paragraph below that link is a section that lists even MORE symptoms that could occur when the quota is reached. I'm sure if I had read the third or even the fourth result, I might have found even more information on what happens, but I leave that to you to explore.