You can use all() or sum() to find out which rows are all zeros. Then use find() to figure out where the last row that has a 1 in it. Then you'll know how far you can shift the rows down. If you pick a random shift, make sure that it's not more than that number or else they'll go past the end of the array.
Here's a start for you:
theSum = sum(A, 2);
lastRow = find(theSum > 0, 1, 'last');
rowsThatICanShift = size(A, 1) - lastRow;
