In the Floating Content application, mobile nodes collectively store and disseminate messages relevant to a certain area by using the principles of opportunistic networking. The system operates in best effort fashion relying solely on the nodes located in the area of interest, which is referred to as the anchor zone of the message. Past work has focused on mobility models, where the nodes are constantly moving and the messages are exchanged "on-the-fly". In this paper, we consider the case, where messages can be exchanged only when two nodes are stationary within each others' transmission range. Our objective is to characterize when the information floats, that is, when it is likely to remain available for long periods of time. We find that there exists a certain threshold for the mean node degree, which we refer to as the permanence threshold, above which the expected lifetime of the information increases very rapidly (in a finite system) or the information becomes permanent (in an infinite system). This threshold is about 1.3 for the basic case (a single stop per visit), which is clearly below the percolation threshold of about 4.5. Additional stops within the zone improve the situation further.