OK, your program has a lot of cases, so it's kind of hard to give a definitive answer, but it basically boils down to this - the front panel retains its information as long as the VI isn't called again. Once it is called again, the new information overwrites the previous information.
One way to work around this would be to make the subVIs VI Templates (simply renaming to *.vit should do) and calling them dynamically. This will create a new instance of the VI in memory which can hold its own data. You will need to manage the references that come from opening the VIs and use the reference if you need to "reopen" it.
Another tip - your code has endless repitions, which you can get rid of. For example, every frame has an Enqueue at the end and a conversion to string. You can get move these out of the case. Some of the inner frames also have a duplicate conversion to string. You can move that out of the frame as well. As a matter of fact, you can get rid of them entirely if you just use the number as the case selector.
Even more so, you can probably create an array with the numbers of states and the strings and search each of the arrays for the current number to know which subVI you need to call. Then, you extract the string from the array and wire it into the subVI. This way, you only have 3 states instead of 112. I'm not sure how well this would work with the vit approach.
Another point, you don't need the queue - simply use a shift register.
One last thing, if you have an error, you should probably do something about it. You can add an error handling case to your machine.
To learn more about LabVIEW, I suggest you try searching this site and google for LabVIEW tutorials.
Here and
here are a couple you can start with. You can also contact your local NI office and join one of their courses.
In addition, I suggest you read the LabVIEW style guide and the LabVIEW user manual (Help>>Search the LabVIEW Bookshelf).
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