There are a lot of myths around vehicle storage and, while some concerns may be valid, most of it comes from car collectors who may drive a vehicle 1 or 2 thousand miles a year. Often those vehicles also have low profile high performance radials that are far more susceptible to flat spotting than the more pedestrian rubber most of us are driving on.
The only flat spotting experience I have ever had was while living in Northern Ontario with winter temps routinely -30 or -40 overnight. Just from overnight it felt like the tires were square and there was no suspension either. I have never heard first hand of any other situation where flat spotting occurs. My truck is used almost exclusively for towing and sits in the garage on concrete from sometime in Nov. to sometime in Mar. My son's Trans Am is a toy and sits even longer and for weeks even in summer. My brother has 3 Corvettes--yeah, I chose the wrong profession--and they sit even more. If we don't notice flat spotting in a vehicle we're driving, I'm not going to worry about it in a trailer I'm towing.
My trailer is stored at home on the lawn on 2X10 planks and I pump the tires up to 60 psi.
Removing the wheels may be a myth too, but one that I will agree with Steve on. No vehicle should be supported by the frame with the wheels left dangling "stretching" the springs. It's just not natural
On my 2499, Sunline specifically indicated the jack points on a drawing in the manual--on the frame about 12-18" from the axles. Unlike a truck, jacking or supporting the axles is specifically prohibited.
So, you would need 4 stands within 18" of the axles to support a typical tandem axle trailer. You have to play with the jack and tongue to try and equalize the weight on each stand so the trailer sits in its "towing position". And you have to have enough support that the jacks don't sink into the ground as it freezes and thaws several times in fall and spring. IMHO, not realistic and not worth the hassle. I would venture that virtually no one who stores their trailer off site bothers with this--there's just not enough benefit.