I've got a set of aero bars on my tourer, and now I've got the hang of them I rather like them, especially when solo and into headwinds or trying to put some distance behind me on a long straight.
A couple of weeks ago I did a rather long ride with a gentle headwind on a fast road at the beginning, so started out by using them rather a lot, and I made good use of them later too. By a rough estimate I used then for over 100km in a day, likely much more. But for a few days afterwards I had real neck ache (DOMS) in the muscles that hold my head up - I'm only a touch lower than in the drops but it seems to make a difference (my bars aren't that low to start with - the forearm pads are ~7 cm below the saddle and they don't stand very high above the handlebar). Yesterday's shorter but still respectable ride wasn't conducive to so much continuous use, but I could still feel those muscles getting tired - no aches today though.
While I try to get some use out of them as often as possible, I'm not happy on them in a group, and my longest regular solo ride is only 30km. So are there strengthening exercises that can be done off the bike? Perhaps something from the long time trial people.