Hi David,

There are many kinds of jasmines. Do you know the botanical name or common name for the jasmine you've tried?
Are you growing it year round inside or are you taking it outside during the summer?
You mentioned over watering. Does the pot have drainage holes? Have you tried the 5:1:1 mixture for potting soil? You can find the recipe by searching for 5:1:1 on this site.
The more information you can provide the easier it will be for someone to answer you.

-Robert

Here is a link that might be useful: Is this the jasmine you've tried?

HEllo Robert,

I do not have the botanical name. But this link:

http://www.whiteflowerfarm.com/83260-product.html

is the one. I have a Confederate Jasmine (larger glossy leaves) that I treat the same way. It has bloomed and thrived annually for years. This one is more lacey and delicate with tiny leaves no more than an inch. I do take it in each winter around late October. The pot has drainage holes and I am using a bonsai soil mixture for better drainage.

Hi David,

You have Jasminum polyanthum which is rather difficult to make it bloom (requires winter temperatures below 60). I'm not familiar with stem dieback but now that we know the botanical name others should be able to help you.
A far easier jasmine to grow would be the Maid of Orleans (the link I provided).
In addition to Sambac Jasmine I would suggest the following jasmines that have a long bloom period (as opposed to the jasmine you are trying to grow which only blooms once)-
http://www.kartuz.com/p/69127/Jasminum+molle.html
http://www.logees.com/Jasminum-azoricum/productinfo/R1920-2/

Good luck!

-Robert

Here is a link that might be useful: Helpful hints for growing your jasmine