I've been towing a single axle trailer for the last 16 years -- two blowouts -- no problem. One blowout was due to delamination of a cheap Chinese tire, and the other was caused by road debris.
Frankly, I would prefer a dual axle -- I think they are safer, but I can't provide proof.
Unfortunately, they don't make dual axle trailers that are as short as mine (12 foot box!), and I really want a short trailer so I can park it in my driveway and so I can boondock in very small campsites.
Life is a series of compromises.
Bear in mind that if you have two trailers the same length, and one has a dual axle and the other is single, the single axle will probably have more storage space. The dual axle wheel wells use up a lot of room.