The larger the screen size, the more memory used, yes, and since current 32bits viewers are struggling with the 4Gb addressable memory limit, it will indeed only increase the likeliness of crashes due to hitting that limit more often.
The Cool VL Viewer does its very best to trap memory allocation failures, but it can't trap everything: implicit allocations done by code generated by the C++ compiler (typically by the "new" allocator in objects constructors, but not only) and/or the std library internal allocations are not trapped: these usually only affect relatively small allocations (which are more likely to succeed than bigger, explicit ones done by the viewer code), but even these can end up failing in extreme memory usage/fragmentation conditions, leading to crashes.