Can my management decide to call anything they want an "essential function" of my job?

I have worked with my company for 18 years no. For the first 16 years my employment was stellar. 2 years ago I got two new managers. I was attending a 4 day seminar in Phoenix and there were only two flights home on the final day. I have autoimmune disease (Rheumatoid Arthritis, Crohn's Disease and Sjogrens Syndrome) and asked if I could leave the final meeting 40 minutes early as the early flight would save me 6 hours in an airport. Important for someone who suffers the fatigue of autoimmune disease daily. I was told no. I should point out that my two coworkers, my peers, the only other people on my team, had asked for and received permission to leave early and had actually left the day before. I couldn't have 40 minutes. I bought the later ticket and then they let us out of the last meeting a full hour early. I could have made the flight so I changed the ticket anyway and ate the cost of it. Since then, anything I ask for or request regarding work travel is an automatic no. Just for me though. My doctor suggested I request a Reasonable Accommodation and I did, asking for permission to make my own travel plans while minimizing any meetings I may miss. I was told no and that every work trip is an essential function and if I cannot do it I am not qualified for the job. Some travel has always been essential: I do mediations and settlement conferences and occasional trials as a Home Office Claims Consultant. I have never missed these and, as a matter of fact, have attended mediation for a coworker who was too ill to travel (it has always been an option). I thought that, for a function to be called essential, a few things had to be true: 1. The job solely exists for this function; 2. There is nobody else there that can do what I do and 3. It has to constitute a hardship for the company. Really, none of these are true and yet suddenly I find myself in the position of knowing that if/when I have a flare up that may impede travel (it has happened twice in 18 years but they have increased the travel schedule this year to make us attend things we never had to attend before) I will be deemed no longer qualified for the job and I will be terminated or demoted. I have a difficult time believing they have not crossed a single legal line. Can anyone help? Do I have any recourse?