Your computer is taking too long to preload and thus timing out on the arena connection. The second time you try it, Windows has all the files in its cache, which copies into AH much faster.
I am going to presume you are preloading skins, which is a problem. No one has a computer with enough RAM to preload all the skins in the game and play the game without swapping. Disable skin preloads.
And if that is not the problem, then something else is amiss. Might need to dump the AH2 cache. There should not be too many files for it to load fresh and make the connection to the arena, unless something has run amok.