The two things in general that create problems for plants in my garden as far as flopping over when blooming are genetics and insufficient sun. Have you tried a different variety (for instance a single instead of a double blossom) and do they get full sun and not a lot of wind?

I'm zone 5 and I have zebrina zebra hollyhocks and they never flop. So if you end up looking for a different variety maybe try this one

David, just so you know, Zebrina/Malva is a different genus and species than what is more commonly called hollyhocks/Alcea, though both are in the same family and have similarly shaped blooms. Malva is a perennial while Alcea is a biennial.