This past weekend I upgraded my Galaxy S5 to Lollipop (including a factory, which is always a good thing to do after such a major Android version upgrade, IMHO). I discovered today that text messages I send from AirDroid are no longer getting split up around 60 characters!
I am not sure if it was the upgrade to Lollipop upgrade, the hard reset, or an update to the AirDroid app (which became available around this weekend also) that happened to solve this problem for me, but regardless I am happy this is working properly now. Hopefully this information will help others with this particular problem, either now or in the future.