It should show up, it may take longer to show up on later rounds. The amount of time is random between some range though. If it is true that it never shows up at all, that might be some rare bug, but I didn't get this bug. Another possibility is that the visual only doesn't show up, though I didn't get that bug either. If you are pretty sure it might be a bug rather than because it was just the time being longer on some rounds, let me know, including how to reproduce it.
It is also possible that because there is some element of randomness, then if you are really unlucky, and didn't use the timer powerup to restore the full time in between rounds, then the amount of time might be so long on later rounds before the target appears that you might lose due to time running out. On other runs, you can just not use anything at all and still win.