The idea from this comes partly from the Medicare Part D prescription coverage "doughnut hole"
In short this is a problem many seniors find themselves in when they lose drug coverage because they've met a coverage limit. However, if their need is serious enough coverage will start again, thus a doughnut hole description.
How this relates to library rules:
I often hear or read or am told about rules in a library that make no sense at all. Sometimes there are rules that say things like, "No Stealing in the Library." My reaction to these is always something along the lines of, "Really, you mean otherwise it was perfectly legal to actually steal in the library?" Other times these might be rules that when I ask around for a reason the response is something like, "What the #@!* does that even mean?" If you want a few good examples of this go see Warren Graham or read his books the Black Belt Librarians.
Now for how this is a doughnut: