Hi Herb,
So glad you responded! Hope you don't mind me requesting that you register, but I've often spent quite a lot of time posting detailed responses to people that aren't registered and never know if they ever get back to look at the info as they don't respond when I ask a question of them. I don't mind lengthy questions at all. Let's see if we can get you some help.
the rain and wind broke (a little more than half way) one of the main branches(there are two)at the bottom of the base. Its still alive but falls to the ground without a stake to hold it up. I was told I should cut it and root it to make another plant.
If the branch has matured enough to have bark (and I suspect it has) you may not be able to root the broken part, but you may be able to root some of it's branches that have softer wood. I would recommend that you take cuttings of the shorter branches. You could still try the taller broken one as well. Here's how to do it with either 'softwood' or 'hardwood' cuttings. If you go to the home page of this site you can find other useful info there as well. Rootone can be found at garden centers. Don't dip the cut ends into the entire packet or jar. Instead put a small amount in a dish or cap and dip into that. Then dispose of the 'used' Rootone when you're done. It's not expensive. Perlite can also be purchased at garden centers where you find potting soil. It's the 'white bits' you find in potting soil.
https://www.trop-hibiscus.com/cprop.html
It only blooms from Nov. thru Jan-Feb. The rest of the year it buds but they either fall off or die I've had it about 3 years now
Bud drop can be caused by stress but it is usually a small insect called a thrip. The thrip girdles the flower's calyx stem where it connects to the base stem. Read 'Biological Control' near the bottom of this page.
https://attra.ncat.org/attra-pub/thrips.html
Here's some pictures of thrips.
https://ipmofalaska.homestead.com/files/thrip.jpg
https://www.cals.wisc.edu/sciencereport/02SR-gallery/Building%20on%20the%20Basics/images/05-Thrip.jpg
I spray it with Orthonex about once a month.
Why do you spray it once a month? Did you see thrips? If so and the buds are still dropping then it could be caused by stress or too much pesticide. I don't use chemical pesticides but I do use organic products. If you are spraying as a preventative, PLEASE stop as you risk poisoning the hummingbirds, bees and butterflies. There is no need to spray unless you have a problem that nature itself can't take care of. For just about every 'bad' bug there is a 'good' bug that will prey on the bad ones. If you just spray you kill the good guys and don't leave an opportunity for balance.
use osmocote fertilizer as per directions and water about once a week.
Osmocote is a slow release fertilizer and I'm wondering how often you apply it. I've found that synthetic fertilizers are like steriods in humans and cause lots of lush growth that can actually 'tire' a plant and leaves behind salt residues. I would suggest top dressing the root zone with an inch or two of compost in spring and fall. You can purchase it in bags.
Compost tea made from compost is fantastic for plant health and can also be used as a foliar spray.
You can also use seaweed or fish emulsion fertilizer that can be mixed with your water. Unfortunately I can't tell you how often to water as I'm not all that familiar with Miami conditions, but if you don't get an inch of rain a week then you might need to water. Deep watering is best so the roots go deep into the soil.
I hope this helps and don't hesitate to ask more questions.
Newt
