This dosn't sound like squirrels to me. They'd rather wait
till the seed starts to ripen. Look for groundhogs. They will pull
down a whole plant to get what they want. They love tomatoes and
cabbages.
To keep birds out of sunflowers make some light cotton bags
like pillow cases and tie them around the flowers before they ripen.
This will help with squirrels but they may learn how to tear through
the cloth.