Hi…
Unfortunately there is no direct way to fix the collapsing mesh from occuring after saving to a figure… 
But there is a work around, and I do mean work around… 
Import the .dae figure into DS… Un-parent the Root from the Scene Root and delete the Scene Root…
Reposition the Root to the floor
Now in the Joint Editor adjust the bone rotation orders… all the bones along the vertical line of the figure should be YZX (head to toes and tongue 1 and 2) leave the rest as XYZ
Then in the Joint Editor Options Menu select Align > Align All Bones then Memorize > Memorize Figure Rigging
Now the work around… 
Re-Export as Colladae (.dae) **this is important, otherwise the rig will seperate from the mesh… 
Clear the scene and Re-Import the .dae figure and un-parent Root from Figure Root…delete Figure Root
Now Export as FBX making sure to check Figure and that it shows in the lower box as a selected figure
Clear the scene and Re-Import the FBX figure… now you may notice that some of the bones do not look quite right… your not seeing things… they have moved…
Now save as a Figure Asset
Clear the scene and load the figure from the Library… the mesh should now be intact and you can go back to the Joint Editor and adjust the bones…
Just remember to Memorize the rigging to set them… also the figure is only using General Weight Mapping, if you prefer, you can convert to Tri-Ax…
Another thing about the Make Human rigging is that there are no Face Groups imported into DS… the joint selection boxes are therefore centered on the joint center points… if you want the bounding boxes to encompass the bones and mesh, then you will need to create the associated Face Groups in the Polygon Editor…
One last thing, you will also need to set all the limits and label the rotation names… and some editing to the weight maps wouldn’t hurt…
Well, like I said… it’s a work around, and the only one I have found other than exporting as .obj from Make Human and rigging from scratch… 
Hope this helps… 