I ran into the same error message a day or two ago with a struct filled with instances of classes that were similarly filled with lots of data. However, I could see in task manager that the memory use was in fact spiking.
The problem went away when I switched to version 7.3 format from version 7 (change file->preferences->general->MAT-Files or I think add flag '-v7.3' to save). This led me to believe that the memory problems might have had something to do with the form of compression done in mat files in version 7.
However, this does not solve another problem associated with save and load which might also cause some issues (it does for me). MATLAB uses lazy copying to conserve memory, i.e. A = B does not make a new copy of B until some part of A is later changed, e.g. perhaps A(end) = 1. Mat files appear to forget about all of these memory-saving relations, increasing both the size of the save files as well as the space required in memory once the save file is loaded.
Hope this helps! Jared