Is it sensible to believe something you can never observe?

Imagine a world, world A, where things proceed normally most days, but every so often, time freezes completely. There are no effects to this freezing of time. Outside observers from another world, world B, are able to witness this event, but unable to communicate it to the inhabitants of World A.

Is it reasonable on World A to believe that occasionally time freezes, to no lasting effect? The first instinct of a logical positivist or Bayesian might be, "no, it's senseless to assert something that cannot be verified, measured or observed and has no lasting effects." Despite my usual affection for these stances on epistemology, I think we can imagine a situation where we might reject this barrier to knowledge, after extending the original hypothetical slightly.

World A, we'll say, proceeds normally for 2 years, but then freezes for a full year every 3rd year. It resumes the pattern the following year, such that it is frozen on years 3, 6, 9 and so on. World B has a similar condition, in that time proceeds normally on it for 3 years in a row, but every 4th year, time freezes. You know this, because you are a scientist observing Worlds A and B from your world, World C.

One day, you build a device to communicate these findings to Worlds A and B. They reply that this is interesting news, as they have seen your world freeze itself on occasion. After working out the math,* it is ascertained that your world freezes every fifth year.

Someone is always watching to make observations for the next several decades, confirming the patterns of freezing in this new era of inter-world communication. And because there is an observer gathering evidence, leaving a lasting record, so far, we haven't caused any problems with those original rigid theories of epistemology.

One day, though, 60 years later, all the worlds freeze at the same time. In that 60th year, we have an event which no one in the system can observe. The event has no lasting effect on the system. And yet, this "system freezing" event seems perfectly reasonable for the inhabitants of the system to believe.

I'm still trying to recall the original source of this hypothetical, it is certainly not my own. I know it is somewhere in one of A. C. Grayling's texts on philosophy...

*No world would observe this simple pattern of the others directly, because the observer would miss a chunk of the observed world's pattern while the observer's world slept. The actual patterns, if interested, would be as follows, and you might imagine a sort of Copernican revolution as they attempted to simplify these patterns:

C watching A sees:
12 year cycle where A sleeps on years 3,5,8 and 10.
C watching B sees:
16 yr cycle, B sleeps yrs 4,7,10,13

B watching C:
15 yr cycle, C sleeps yrs 4,8,12
B watching A:
9 yr cycle, A sleeps yrs 3,5,7

A watching C:
10 yr cycle, C sleeps yrs 4,7
A watching B:
8 yr cycle, B sleeps yrs 3,6