Their story was a very complicated one. They started off as an unlicensed fan group. They sold sponsorships to businesses, where BOA members received discounts, specials, etc.
Then, they paid UT to license the Power T and Lady Vol T for their promotional interests. The UTAD cut them a really good deal because of the increased fan involvement that they saw could come of the idea. This allowed them to sell the army helmets with the Power T on the side. They also used the logos for stickers, t-shirts, jackets, etc.
My timeline on this next part may be a little off, but things happened in quick succession.
A controlling interest in the BOA was purchased by Action Sports Media, which was bidding on the UT Media package held at the time by the Vol Network/Host. Action expanded the sale of BOA sponsorships, and the businesses that sponsored now displayed the "new" BOA logos that featured the Power T and Lady Vol T, which was, in UT's opinion, a violation of the licensing agreement for the logos. Basically, Action was selling sponsorships to local businesses for much less than UT and Host were, and the businesses were using the BOA logo as if they were UT sponsors. The UTAD ordered them to stop, and Action did, after a short battle.
Action then lost their bid to take over the media rights in 2006 (which included a totally new sponsorship sales structure for all platforms, making top-level Vol Network sponsors UT corporate partners, and vice-versa) to Host, which was later merged with IMG. Action stepped back from the BOA and largely exited the market.
The final straw with the BOA was their "Fort Neyland" ad campaign. There were two issues with this. First, the BOA licensing agreement didn't cover the Neyland Stadium name or likeness, which they had plastered on billboards all over town. Second, the Neyland family thought it was in extremely poor taste to use the name of a war hero in a pseudo-military ad campaign. They found it offensive. Turns out, the family had been uncomfortable with the whole Big Orange Army idea all along, but had avoiding making it an issue until the family name was made into a caricature on billboards.
UT ended up taking the BOA to court over it because they refused to take down the billboards and stop selling the t-shirts, even after UT canceled the licensing agreement. In the judgment against the BOA, all BOA trademarks were surrendered to the UTAD, which killed them.
Edit: At some point in 2010, after being "dead" for almost three years, UT allowed the original founder to reclaim the logos and name for very limited usage after Action Sports folded. He has a license, but I haven't seen them doing anything with it recently.