In this case I would utilize a Singleton, created when the user first needs to read itor write data, backed by a database. This Singleton could be provided through a dependency injection framework (and thus not be a real Singleton) but it depends on what xamarin can offer you.
Singletons are generally bad, but only because they tend to be overused and there is often a better solution to a given problem.
I am not sure what tools xamarin give you to work with a database.