Just playing devil's advocate here. But the AA do say that the vehicle (read trailer) must be kept in a roadworth condition and maintained in line with manufacturer's specifications.
They are getting tighter regards their conditions of service. I used to run a Suzuki SJ410 many moons ago and I must have called them out 3-4 times one year. I received a letter to indicate that I may be refused membership or possibly charged for the next call-out. I wrote a letter to them saying the the faults were all unrelated, the car had a full MOT and I'd been a member for 10+ years. Got a nice letter back to say sorry.
Wouldn't be without them.
Luckily the trailer axle didn't break on a motorway. But I can see your frustration. Get a letter to them to see what they say.