Depth isn't an issue with embeds and neither is URLs, so if the embed works from template A, it will work from Template B. So it isn't any parameter issue (unless you use embed variables in the parameters - see 2 below).
Three factors that are most likely:
- The embed in Template B is within a conditional which is not being met.
- You're passing embed variables from template A and incorrectly passing them to Template C from B.
- There's a error in Template C which means it doesn't render (add-on?) - dump a test string outside any channel:entries tag pair to check if the template is accessed at all (this is also a good test for no. 2).
Seeing as we don't know your template code, I'm going to guess at no. 2 as being at fault (it's the one that usually catches me out the most).