Edited to add:#More generally, ever-increasing number of backups are needed for arbitrarily long timespans
Ultimately if you are concerned about your civilization preserving the information indefinitely on cosmological timescales (as suggested by your comment about assuming they can avoid heat death and proton decay), you will want the civilization to periodically make new backups and store them in different locations throughout the universe, so that the probability that all records of some information are destroyed is continually decreasing over time. If the probability of all records of some information getting destroyed isn't decreasing this way, if you wait long enough it becomes a virtual certainty you'll lose that information. Say in a given million-year timespan the probability is $q$ that the civilization loses some item of information due to all records of it getting destroyed, so the probability the information is preserved in that timespan is $(1 - q)$. Then naturally if the probability is same in the next million years the total probability the information will be preserved for 2 million years will be $(1 - q)*(1 - q) = (1 - q)^2$, if the probability remains constant for 3 million years the probability the information is preserved in that time is $(1 - q)^3$, and so forth. No matter how close $(1 - q)$ is to 1, there's going to be some sufficiently large exponent $N$ such that $(1 - q)^N$ becomes arbitrarily small.
On the other hand, suppose the probability the information is preserved in the first million years is still $(1 - q)$ but the probability it's preserved in the next million year span is $(1 - q^2)$ and the probability it's preserved in the next million year span after that is $(1 - q^3)$ and so forth. So here the probability the information is preserved for 3 million years is $(1 - q^1)*(1 - q^2)*(1 - q^3) = \prod_{k=1}^{3} (1 - q^k)$, using Pi notation for products akin to Sigma notation for sums. Then if that pattern continues indefinitely the probability the information is preserved approaches a nonzero limit $\prod_{k=1}^{\infty} (1 - q^k)$, which according to this mathematica page is given by the Euler function $\phi (q)$, and the page also shows a graph of its value for different values of $q$. So this limit can be thought of as the probability the information is preserved forever, assuming a universe where a civilization surviving forever is physically possible (I talked about that question in this answer, and where they are able to create an ever-decreasing probability of losing all copies of some record by the method of ever-increasing numbers of backups.
