We report on continued monitoring observations of the Galactic center carried out by the X-ray telescope aboard the Swift satellite in 2008 and 2009. This campaign revealed activity of the five known X-ray transients AX J1745.6–2901, CXOGC J174535.5–290124, GRS 1741–2853, XMM J174457–2850.3 and CXOGC J174538.0–290022. All these sources are known to undergo very faint X-ray outbursts with 2–10 keV peak luminosities of LX,peak ~ 1034−36 erg s-1, although the two confirmed neutron star low-mass X-ray binaries AX J1745.6–2901 and GRS 1741–2853 can also become brighter (LX,peak ~ 1036−37 erg s-1). We discuss the observed long-term lightcurves and X-ray spectra of these five enigmatic transients. In 2008, AX J1745.6–2901 returned to quiescence following an unusually long accretion outburst of more than 1.5 years. GRS 1741–2853 was active in 2009 and displayed the brightest outburst ever recorded for this source, reaching up to a 2–10 keV luminosity of LX ~ 1 × 1037 (D / 7.2 kpc)2 erg s-1. This system appears to undergo recurrent accretion outbursts approximately every 2 years. Furthermore, we find that the unclassified transient XMM J174457–2850.3 becomes bright only during short episodes (days) and is often found active in between quiescence (LX ~ 1032 erg s-1) and its maximum outburst luminosity of LX ~ 1036 erg s-1. CXOGC J174535.5–290124 and CXOGC J174538.0–290022, as well as three other very-faint X-ray transients that were detected by Swift monitoring observations in 2006, have very low time-averaged mass-accretion rates of ⟨Ṁ⟩long ≲ 2 × 10-12 M⊙ yr-1. Despite having obtained two years of new data in 2008 and 2009, no new X-ray transients were detected.