We have only done a special needs request once, on Rhapsody, and it was not honored. Needed a medical fridge and not only was it not there, no one seemed to believe they exist. We were in a suite, and everyone from room steward to concierge to guest services swore up and down that RC does not provide them. So, like sross6019, we ended up juggling ice and zip locks the whole week. Very unpleasant. I got a special needs email when we got back asking if we were happy, and I replied immediately with a "since you ask...." Got a very nice credit towards next cruise.
The steward did offer to take the meds to staff fridge, but given how expensive they are, and the very small temp window that is allowed, did not feel we could do that. However, on the last day I thought to ask her to freeze the gel packs we had used on the plane so we had them on disembarkation. This worked very well, and if we face this situation in future, I will pack extra gel packs for the purpose of switching out. I know how long those last and wouldn't worry as much as I did with melting ice.