Cruise prices are dynamic, and they can sometimes drop if demand for a particular sailing.

Similar to hotel or airfare, prices fluctuate and we can see prices go down in some situations, even after you've booked a cruise.
Cruise fares going down aren't that common, but it sometimes happens.
When there is a price drop, there could be the opportunity to save money, but it depends on a few factors.
When do Royal Caribbean cruise prices drop

Because Royal Caribbean uses dynamic pricing for its fares, a specific fare could go down in price if the factors warrant it.
The cruise line doesn't inform guests that are booked there has been a change in price, so it's up to the consumer to track it.
There are all sorts of reasons for a price drop, but it's usually tied to unsold cabins.

If there are too many unsold cabins, cancelled reservations, or the pace of new bookings isn't where the cruise line wants them to be, a price drop could be employed to spur sales.
In fact, price drops can be hyper focused on a specific cruise room category for a given sailing. It's rarely, if ever, across the board. You should never expect a price drop in the same way retail products are discounted where prices are slashed for everything.
Some cruisers will point out there are price drops around the final payment date, which is 90 days before the scheduled departure. That's because of last minute cancellations made before the penalties kick in to cancel.

I find the most consistent types of cruises that get a price drop are long sailings, such as repositioning's or transatlantic crossings.
In short, there's no specific time a price drop will or won't occur, but it could happen at any point.
If you're past final payment date, there's nothing you can do to get that better price.
You might be able to re-price a cruise if there's a price drop

You might be able to take advantage of a price drop, but it depends when it occurs and your residency.
Residents of select countries can price match the lower price with no penalty at the lower rate if:
- The price drop is for the exact same stateroom category code on the same ship and sail date
- It's before final payment date
- You're a resident of certain countries, such as the United States or Canada (there are other countries too)

It's up to you to spot the price drop and then request it.
There's no means for consumers to reprice the cruise, it must be requested. If you booked with a travel agent, the agent can do it. Otherwise, you have to call in and request it with the cruise line.
A word of warning, I've heard from many readers who have called Royal Caribbean to ask for a reprice and told it's not possible. Assuming you've adhered to all of the requirements mentioned earlier, it could be someone unfamiliar with the repricing option. Trust me, it's exists.
How to check if Royal Caribbean has a price drop

The way I look to see if there's been a price drop is to do a mock booking for the cruise I'm booked on.
Basically, going to the Royal Caribbean website and going through the steps for booking a cruise to verify the price.
It's important to be checking you've got the same exact cabin category down to the stateroom code. That means not just looking up the price of a balcony, but the category code that's a number and letter combination (i.e. 4D).

Mock bookings are simple, but it's also manual. You have to take the initiative to check, and prices could change at any time.
Some travel agencies will check for you, but I've found it's rare.
As an example, MEI Travel has an automated tool that periodically checks for a lower price and then alerts the agent so they can make the change even without their client requesting it. (Disclosure: MEI Travel is a sponsor of this site)

It's important to also remember when repricing to consider any onboard credit or freebies you have, as those would potentially be lost.
Repricing is effectively booking a new reservation, and you cannot carry over any promotions Royal Caribbean may have offered from the initial booking to the updated one. NextCruise offers, however, would still apply.
Booking early is a good strategy

I always try to book my cruise early and then keep an eye out for price drops later.
Usually the lowest cruise prices are when new sailings go on sale many months or years before the cruise depart. It's not uncommon that I never see a price drop because I already booked the best price.
The strategy of booking early and then taking advantage of price drops ensures you always have the lowest price, as opposed to trying to time a price drop later (which may or may not happen).

I would never purposefully wait to book a cruise so that I could time a better price. Once I know I want to sail, I'll book immediately and then message my travel agent if there's been a price change.
Because cruise fares seem to only be going up due to ever increasing demand, I don't see that many price drops. More often, it feels like prices simply rise as the sail date approaches.