Hi Everyone,
I wanted to report my experience here as I thought you all would probably be able to understand it far better than I can, and maybe even find it interesting. I'm a newbie, so bare with me...
For the longest time, I was using the UIPEthernet library 'improperly'. I wanted to open a connection and keep it opened(indefinitely if necesssary), and "stream" my data to my program - a long string of text parameters, about 200 bytes. The easiest way to do this seemed to be just simply not disconnect. Using the basic examples as a starting point however, this results in the need to "ping" the Arduino every time you want data, resulting in a perpetual game of "ping/pong". The connection never actually closes, but using client = server.available(); to call your actions causes this I guess, since it only returns 1 if there is data waiting to be read. This is what all of the examples seemed to use, so I thought it was the right way. Adding fuel to the flames, I found a blog that seemed to call this a bug, and showed how to fix it with the stock Ethernet library, so I thought I was on the right track. I wanted to use UIPEthernet though, and the ping/pong scheme seemed workable, if kludgey, so I implemented it. I had it working for a long time - a couple of months - without any trouble overall. I mean, I could open a telnet session with PuTTY and have it sit there open for days and randomly "ping" the arduino and get a packet.
However, I just knew it didn't seem right, and like I said it was kludgey, made all of the other things I was having the Arduino do all the more difficult. I wanted to fix it, to the point of making a fool of myself asking about it on the Arduino forums.
So anyway, after studying some other examples for a while, and reading some other things, I figured out the "proper" way to do things - store your (up to 4 connections) in an array; that way you can check them for (dis)connections, send data to individual ones, etc. Elementary I assume, but like I said .. you gotta start somewhere. 
Fantastic! No more pinging!
Except now I've lost the stability I had. Couldn't keep a connection for more than 12 hours it seemed, let alone the days and weeks I had before. Frustrated, I basically dropped the project for a couple of weeks. The other day I decided to pick it up in earnest again. I couldn't find anything wrong with my code after going over and over it, so I hit google again..
This thread came up, and seemed pertinent. I installed the fix version of the library, and what do you know - stability. 
Been almost 48 hours now. Nothing else has changed, so I'm going to call it fixed. I don't really know what to make of all that, but I find it interesting that I had such great stability using the first method overall, even though it was "wrong".
I want to thank everyone for their efforts, especially Norbert for the superb support of his library. It truly makes it a pleasure to use. I can only hope I can contribute to the general community on such a high level one day.
Edit: 72 hours+ and still going strong.
