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The rotation in the ribbon and in the project environment work in different ways.
The one in the ribbon you point to the point of rotation and rotate the whole component around this point.
The ones in the project environment are component/family internal rotations. Basically you ask to rotate the connector.
At that point revit will calculate how everything relating to that connector have to be modified and starts recalculating the different parameters.
At this point it goes wrong. Due to the requested rotation some of your instance parameters will be recalcualted/modified and result in a new value that will not allow the component/family to be created.
Therefore you would have to constrain your family so that it will not result in "impossible" parameter values.
Things to consider are:
-Less instance parameters and more type parameters.
-More relations between the parameters so that impossible values can not occur
-Make use of nested elements to simplify things.
Louis
Please mention Revit version, especially when uploading Revit files.
As far as I can see it, the problem remains the same. One rotation might be possible because the (changing) instance parameters stay within certain tolerances that it will aloow to construct the component. The second rotation then start altering the instance parameters again ending in impossible values that will not allow revit to construct the component.
I think you would have to make the following consideration. Do you really need/want to have that many instance parameters.
For example can you consider to make several of the instance parameters into type parameters?
Than you could offer the user several different types (if needed). Most of the components would be in the real world also limited to several different types.
If you really want to have that many instance parameters you would have to do major troubleshooting. Basically you want to controle the parameters so that they will not generate errors/impossible values. There are different approaches to this problem basically involving compartmentalizing the issues.
1-Use several nested elements. You can test each nested element alone and check that it will work in "all" instances. As final step bring the different nested parts together into s asingle family.
2-Change all your instance parameters in type parameters. Basically you have now a fixed model. Check that it will work/rotate in the project (should be Ok).
Slowly start changing the type parameters back to instance parameters. With each change check if it still works as expected. As soon as it start to break you get the idea which parameter is behaving badly and you can try to constrain that so that it will stay within allowable limits. Continue the process.
Not the most fun task and not solved in few minutes. But the more flexible your model gets, the more testing has to be done.
Louis
Please mention Revit version, especially when uploading Revit files.
2-Change all your instance parameters in type parameters. Basically you have now a fixed model. Check that it will work/rotate in the project (should be Ok).
I listened to your advice and I changed all instance parameters into type parameters..and I came to conclusion that the only problem is parameter b...when I put the parameter b to be type parameter everything works fine...but parameter b is pretty important to be instance parameter 
Did some experiments. The connectors you used are directly linked to your model dimensions. So when pressing the rotate button on the screen it starts modifying all the instance parameters (a,b, h etc).
What seems to help is if you dimension the connectors indirectly. So instead of having parameter "a" directly coupled to the height of a connector use a new parameter (e.g. Connector1_Height). Do similar things for all the connectros (height & width). In the parameters create simple formulas (e.g. Connector1_Height = a). It seems strange as it looks exactly the same. However internally revit seem to build the model a little differently and seems to work. Can not send you the modified family as I am using revit 2015.
Hope it works for you.
Louis
Please mention Revit version, especially when uploading Revit files.
Can you elaborate?
When I have a piece of duct, select the Tee from the project browser and place it against the duct it sizes accordingly.
Here in screenshot I started with 3 pieces of duct 400x400, 400x600 and 400x800.
Took the tee from the project browser and put it against the duct and it resizes the tee without a transition (see screenshot).
Maybe you have a different workflow? Or I am missing something.
Louis
Please mention Revit version, especially when uploading Revit files.
Oke, unfortunately no quick fix then. Then basically it would mean that you will have to delve deeper in the family.
In your family you have many reference reference lines and parameters. This will make it complicated to differentiate and keep track.
Therefore I would modify the family. I would propose to make use of nested families. You could put each branch in a separate family. Make sure that it flexes properly and everything is constrained. Than the two branches can be put in the host and control the nested families. If needed you can create multi nested families (e.g. flange as separate family nested in the branch family).
An advantage of this approach is that it will become more predictable. Revit will start building fitrst the nested families before positioning the nested families in the host.
Louis
Please mention Revit version, especially when uploading Revit files.
Your clue got me thinking. I did some addtional testing.
What I see is that if the default value (height) of the Tee are larger than the values of the duct than a transition is added.
When the tee its default value is less than the size (height) of the duct it resizes the tee.
I changed the default values of the Tees so that the height became less than 400 mm and it started to resize the tee when connecting.
Therefore you should make your Tee's default values as small as possible without breaking it before inserting it into the project..
I think these are the small quirks of Revit. I believe it is an internal priority sytem that determines how such cases are handled.
I would be interested to know if you will see the same with your version of Revit.
Louis
Please mention Revit version, especially when uploading Revit files.
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