Never! Fun answer to a fun question, I know, but think of ancient currency this way: Rather than a coin specifically detailing who was a ruler or governor at the time, the coins were stamped with an "I minted this." Coins minted by a specific emperor retained all of the monetary value of the coin's type- five ounces of gold are five ounces of gold, no matter whose face is on them. The one notable exception to this rule was if an emperor was declared damnatio memoriae, in which case everything alluding to them was proactively destroyed. It wasn't 100% effective, but it certainly makes archaeology for some people (Caligula, Heliogabalus...) pretty difficult!

Going a bit beyond your question, but during the Republican period (c. 500BC-AD), minting coins was a huge honour for your entire family, and most of them didn't put their own faces on coins. The faces of old kings would appear, Roman legends, gods, symbols...but never their own face until Julius Caesar. These coins, as with those of the early Empire, were in use indefinitely. Of course, a small problem happened in the middle of the Empire: inflation. Coins became diluted with lesser metals to the point where, during the Crisis of the Third Century, prices skyrocketed to the extremes. For example, a normal day's wage in the early Empire was about 1 denarius (4 sestertii), which was enough to buy a cheap prostitute or a really nice wine - a Falernian. By the time Diocletion attempted to standardize prices (300ish AD), the price of that same glass of wine was now 30 denarii. So, while the currency was never replaced, per se, it became much less valuable over time, especially because bread merchants weren't going to necessarily know the exact ratio of valuable metal in the certain coin that you might give them.

Hope that helped a tiny bit!