Fluid antennas offer a novel way to achieve massive connectivity by enabling each user to find a 'port' in space where the instantaneous interference undergoes a deep null for multiple access. While this unprecedented capability permits hundreds of users to share the same radio channel, each user needs to switch its best port on a symbol-by-symbol basis, which is impractical. Motivated by this, this paper considers the scenario in which the fluid antenna of each user updates its best port only if the fading channel changes. We refer to this approach as slow fluid antenna multiple access (s-FAMA). In this paper, we first investigate the interference immunity of s-FAMA through analyzing the outage probability. Then an outage probability upper bound is obtained, from which we shed light on the achievable multiplexing gain of the system and unpack the impacts of various system parameters on the performance. Numerical results reveal that despite having a weaker multiplexing power than the symbol-based, fast FAMA (i.e., f -FAMA), spatial multiplexing of 4 users or more is possible if the users' fluid antennas have large numbers of ports.