Mary, not just 3rd parties but the management of the Colosseum/Forum/Palatine themselves can cancel their own tours due to strikes, weather, repairs or other complications. For instance, this just popped up on the coopculture website last week:
CLOSURE OF ARENA, UNDERGROUND AND THIRD LEVEL
Due to the complex setting-up and taking down of the Via Crucis during the Holy Easter, from April 1st until April 12th the access to the arena, the underground and the third level of the Coliseum will be closed to the public.
Last year, the Italian Ministry of Culture announced National Museum Culture Week, when entry to all state museums/monuments would be free, with such short notice that the museums themselves, as well as the tour companies, were caught out. As no tours are generally allowed during free-entry days, there was a lot of scrambling to refund bookings!
As well, 3rd parties have to acquire tickets same as individuals do. Sometimes they can't get them for a particular day or time so will offer an alternative to the day/time booked or a refund. Pretty much all of them I've looked at have disclaimers somewhere on their websites to cover that possibility. Here's Roman Guy's disclaimer (under the FAQs):
Can my tour be canceled or moved to a different day?
Yes. Obtaining reservations for this tour is a complicated process, but we are the best at doing it! However, sometimes we don't always secure reservations for every day. While this is rare, it does happen. We will let you know at least 7 days prior to your tour if this is the case for you. You'd be entitled to 100% refund and we would do our best to move you to another one of our incredible restricted access tours! We got you covered!
Is it possible The Roman Guy will change this tour time?
Yes! It is possible. This tour is highly coveted and the reservations are hard to get. This is an industry challenge for tour companies. Times often change by a few hours and we will almost always update you at least 7 days before your tour. We really want you to be happy as a traveler and will do our best to meet the needs of your schedule. That being said, we are limited by a very low supply from the Colosseum. If necessary, The Roman Guy will call the number you've provided or email you with the goal of informing you of this change. If you are nervous about keeping up with time-changes we recommend booking a different Colosseum Tour. If you want to make sure your Colosseum tour is going to run as scheduled please email or call +1 888 290 5595.