Do you weight the bottom at all or just leave it a smidge thick for balance? The couple of deeper things like that I made were a bit tippy but I also was perhaps a bit more aggressive at hollowing than I should have been.
The base is left about 20mm thick for weight, normally adequate for dried or silk flowers etc.
On larger pieces where taller hedgerow subjects are used making them less stable we usually put glass or ceramic (baking) beads in the base, even sand.