Unfortunately, this is what happens to many of us that suffer from anxiety. We find a benzo that was made for us (cures our anxiety) and then the doctor decides we've been on it too long and quits prescribing it. If you are not depressed and your anxiety is controlled with the Xanax I don't see why you can't continue to take it. Xanax is a perfect drug for persons with severe anxiety. I guess SSRIs are the new fad right now with so many of them coming out on the market that doctors are bombarded with drugs reps informing them of the tragedies of patients on Benzos for long term therapy and they need to switch them to SSRI drug therapies.
The same thing happened to me when I went on Paxil. I asked the doctor for Xanax and he informed me that this med was addictive and he would prefer that I take an SSRI because they are not as addictive (some people would disagree). I can say that after I got the Paxil in my system I did not need the Xanax anymore.
I would give the Lexapro a go. Ask the doctor if you can still take the Xanax (3 times per day) for a month at full dose while the Lexapro takes effect. You will have to discontinue the Xanax slowly and I would not try to discontinue until the Lexapro has been in your system for at least a month if not longer. SSRIs will sometime give you more anxiety, stomach upset, diarrhea, etc. at first, however, these side effects go away after about a month. You need to give the Lexapro at least a couple of months to work.
Or you could go to another doctor that will let you stay on Xanax; however, eventually, most doctors, will not want you to stay on a Benzo long-term.
I took Xanax a long time ago as prescribed (2 times a day) and after 6 months I came off it slowly and did not have any withdrawal side effects. I was taking Lexapro at the time so this helped with the withdrawal from Xanax.