But, if n >> the life of the clock, then no, it will never be correct.

After the life of the clock, it will be stopped, and thus right twice per day.

As you said, it may take a very long time to lap the clock, but once you stop drawing distinctions between "never" and "sufficiently infrequent", you get into the question of acceptable precision. Most people would consider an analog, two-handed clock to be "correct" so long as it is accurate to the minute. That means the threshold of tolerance for a "slow" clock would be the loss of at least one minute per 12 hour period to remain "incorrect". That means you'll lap the clock, and it will be correct, every 720 cycles, or about once a year.

If it loses time faster, you'll lap it faster. If it loses time slower, it will spend more consecutive cycles as "correct" within acceptable tolerance. It's possible to devise a mechanism which alternates between running fast and slow to ensure that it is actually never correct, but that would have to be built as an accessory mechanism on top of a functioning desynchronized clock in order to ensure that it's really never.