ATT goes down much more frequently than Verizon because of the way their 3G network works and because there are probably more ATT subscribers at the stadium. Long technical mumbo jumbo could be used to explain the problem, but more interestingly, there are some ways around it. I hesitate to share them here as they become less reliable as more people use them, but I am a good guy, so lets all just keep this a secret. It's not like this is going to get out. It's only the internet right?
The easiest way to retain/regain cell reception at LVES is to...here it comes...wait for it...TURN YOUR 3G RADIO OFF. This will force your phone to connect to ATT's older EDGE network (2G), which is probably going to be less populated and therefore more reliable. If that fails, and if your phone allows, you can turn off EDGE service and you will be relegated to ATT's older network (think it is GSM around here-not sure about that though. Could be GPRS) which will likely be even less populated.
I try going to EDGE first, and that usually works, but if not, I just turn off EDGE as well. Data is still very slow/non-existant (just like in the good ol' days), but I can text and call without problems.
I'm not sure to what extent different phones allow you to selectively turn off radios. I imagine that they all will let you as it is very helpful in improving battery life, among other things, but they might just try to hide it in the settings under something like, "turn off data connection" or something like that. I have an iPhone. It is jailbroken and I use a jailbreak app called SBSettings that lets me control all of that very easily and without doing anything technical. But even "dumb phones" nowadays connect to the 3g network to make calls, so turning off 3g with those is also helpful.
BYU definitely could install extra hardware to alleviate this problem. In fact, they already do in several buildings on campus where reception is poor etc., but only for Verizon. This is done at BYU's request and on their dollar. They could do the same at LVES if they wanted to.