We study the periodic solution of a perturbed regularized Boussinesq system, namely the system $ \eta_t + u_x + \beta (-\eta_{xxt} + u_{xxx}) + \alpha ( (\eta u)_x + \eta \eta_x + u u_x ) = 0, u_t + \eta_x + \beta (\eta_{xxx} - u_{xxt}) + \alpha ( (\eta u)_x + \eta \eta_x + u u_x) =0,$ with $0<\alpha, \beta \leq 1$. We prove that the solution, starting from an initial datum of size $\varepsilon$, remains smaller than $\varepsilon$ for a time scale of order $(\ varepsilon^{-1} \alpha^{-1} \beta )^2$, whereas the natural time is of order $\ varepsilon ^{-1}\alpha^{-1}\beta$.