Question: I want to create a field in a template (dotx) that, when starting a new document from that template, would prompt for information. The field is something that repeats over and over in the document. I want to be able to enter it once and that it would update itself across the document.

Answer: 
I was able to just use simple FILLIN fields for my application, but I was having a hard time getting my prompt windows to appear when opening the document. I didn't realize that I had to save the word document as a template (.dotx) before it would work. After I did that it worked great!
I just tried to get the FILLIN merge field to work per the instructions and couldn't get it to work. A less complex way is to use the STYLEREF merge field. To do this, create a generic field name for the first instance of the data (e.g. "organization" or "date") and create a unique style for it (for the purposes of these instructions, I'll call it "Style1"). At each place in the document where you want the data to repeat, select ctl+F9 and insert STYLEREF "Style1" between the brackets (it will look like this: { STYLEREF "Style1" }. So long as you don't disassociate the style from the first entry. Note, don't use the style you've used for anything else but for that merge field. Word populates this merge field from the last know entry for the style.