Hi Vadim,
Welcome to our Mattress Forum! 
[quote]More recently, we used the same type of mattress on adjustable bed (LP iEscape) bed, and ran into two problems: (1) the adjustable bed does not appear to provide the same support as we are used to with a platform bed, and (2) the adjustable platform is actually 2 inches narrower than the state size (58’’ vs 60’’ on queen). As the result our mattress feel very soft and sloping down on the sides. Very disappointing experience.
Hence my question: are these two problems generic with all adjustable beds, or did we just made a porr choice?[/quote]
A quality latex mattress is generally a great fit for an adjustable bed as latex can be moved, folded, and adjusted in any direction one desires. Latex is highly flexible and follows the contour of what is set on. You are mentioning that you are using “the same type of mattress” so I am not clear if you are using the same mattress, if it is a different mattress then it is likely that this is another contributing factor.
I have no experience with the iEscape and I was not able to find out if the decking is solid or slatted but assuming that you are sleeping on the same mattress, in a flat position and that the decking on the steel frame is solid then it should perform similarly to the latex sitting on a platform bed or on the floor. The 1" edge support missing on each side of the mattress should not impact the support you are experiencing when sleeping upon it but I do see how this would cause a “slopping down on the sides” as it would be missing some of the edge support you are used to.
I was able to find that some retailers listed slightly smaller dimensions for this model but I do understand it is disappointing when specs are not exact.
To check all your bases, I would make sure to inspect the underside of the unit with a flashlight when the unit is under heavy load (mattress and person) to determine if there are any loose parts or bending of decking.
I’d suggest that you take a look at the first post in this thread titled “The Best Foundations or Base for a Latex or All Foam Mattress” which may give you more insights. Post #2 in this thread discusses the other features of an adjustable bed that may be important to consider and post #6 here has comparisons between popular adjustable bed bases. that may be of interest.
Phoenix