I'm presently using TCMD 16, but I had a similar problem a while back.
I had my 4start.btm downloading and parsing a web page, putting some of the info into environment variables, and then proceeding to the prompt. No problem for a long time with that. I then started experiencing a similar problem to yours, where it would take several minutes for the prompt to appear. After much frustration, I took a look in my 4start.btm, and remembered about the web page parsing. Turns out there were problems with the web site being quite slow, which, in turn, delayed the command prompt from appearing.
Another problem I had was in my post_exec.btm. I have several things going on which were not convenient to put into the post_exec alias. So, my post_exec alias simply points to c:\utils\post_exec.btm, where I have many things going on after returning from a command prompt, and before displaying the prompt.
One of the files that I work with in my post_exec.btm got knackered one day, causing a lengthy delay. Again, after much frustration, I remembered about my post_exec.btm, found the problem with the file, corrected it, and all was well again.
These may not be the cause of the problem that you are having, but just passing on what has caused my command prompt to be very slow in appearing.
Thanks Joe for sharing your experience. Mine seems to be something different as I don't have any such .btm processing. One thing I noticed is that if I start up a new Windows command line window, it gets added as a new tab in TC and gets the prompt right away while other tab is still waiting for prompt.