Many or most cases of 'tendonitis' are in fact tendinosis; consequently the problem is not inflammation and damage to the achilles, but instead a neovascularization - blood vessels have grown into the tendon and causing swelling. I have had this problem off-and-on for two years and dealt with and continue to deal with it through excentric training. With the initial problem two years ago I finally was able to see one of the top specialists for tendon and especially achilles injuries (Alfred Håkansson, if you are interested in searching for his research papers). The basic idea is that through excentric training - standing on a stair, raising your weight up using both feet and than gradually lowering your heel while standing on just the one foot - you shear off those vascularizations. The problem is that if you are fit then body weight is not enough and you have to load weight on your back. His recommendation was to use as much weight as you can stand - it will hurt. I use 15 kg in a pack just for maintenance excentric stretching, but when problems begin to increase the load will increase to 30-40 kg (then I do this in the gym). The other important factor is doing this with dedication; when I first had serious problems I would do 15 kg loads at home (3x10reps for each leg - to keep it balanced) in the morning and evening and pass through a gym at the university at some point during the day for a heavy set, building up from 15 to ultimately 40 kg. It took 3-4 weeks to have a noticeable effect.
I was very sceptical this would work, but in the weeks I was waiting for surgery (where he scrapes the inner side of the achilles to shear off these vascularizations) things turned around after 4 weeks. Surgery was first tentatively delayed, but after the improvement started we agreed to cancel it.