A hypergraph is a generalization of an ordinary graph, and it naturally represents group interactions as hyperedges (i.e., arbitrary-sized subsets of nodes). Such group interactions are ubiquitous in many domains: the sender and receivers of an email, the co-authors of a publication, and the items co-purchased by a customer, to name a few. A higher-order interaction (HOI) in a hypergraph is defined as the co-appearance of a set of nodes in any hyperedge. Our focus is the persistence of HOIs repeated over time, which is naturally interpreted as the strength of group relationships, aiming at answering three questions: (a) How do HOIs in real-world hypergraphs persist over time? (b) What are the key factors governing the persistence? (c) How accurately can we predict the persistence? In order to answer the questions above, we investigate the persistence of HOIs in 13 real-world hypergraphs from 6 domains. First, we define how to measure the persistence of HOIs. Then, we examine global patterns and anomalies in the persistence, revealing a power-law relationship. After that, we study the relations between the persistence and 16 structural features of HOIs, some of which are closely related to the persistence. Lastly, based on the 16 structural features, we assess the predictability of the persistence under various settings and find strong predictors of the persistence. Note that predicting the persistence of HOIs has many potential applications, such as recommending items to be purchased together and predicting missing recipients of emails.