Two coupled nanolasers exhibit a mode switching transition, theoretically described by mode beating limit cycle oscillations. Their decay rate is vanishingly small in the thermodynamic limit, i.e., when the spontaneous emission noise tends to zero. We provide experimental statistical evidence of mesoscopic limit cycles (∼10^{3} intracavity photons). Specifically, we show that the order parameter quantifying the limit cycle amplitude can be reconstructed from the mode intensity statistics. We observe a maximum of the averaged amplitude at the mode switching, accounting for limit cycle oscillations. We finally relate this maximum to a dip of mode cross-correlations, reaching a minimum of g_{ij}^{(2)}=2/3, which we show to be a mesoscopic limit. Coupled nanolasers are thus an appealing test bed for the investigation of spontaneous breaking of time translation symmetry in the presence of strong quantum fluctuations.