If energy can be converted into mass then why isn't photon's energy being converted into mass?
You probably mean something different than you ask: a photon is influenced by gravity and it behaves as it had a mass when traveling through the space. When it is said that photon is a massless particle, it is in a context that it has no rest mass $m_0$ i.e. $E^2=m^2c^4=p^2c^2 + m_0^2c^4$ turns into $p^2c^2$ ($p$ is momentum), but $mc^2$ still speaks about the amount of its gravitational interaction.
I have also a funny answer (slightly less correct) - based on recent Ethan Siegel's popular article: photon is converted into mass (or something) instantaneously. Since the photon travels by velocity $c$, it itself (because of special relativity) doesnt experience the time flow and its birth and death are (from his own point of view) instantaneous.
Maybe you mean what you really tell, but then it is a discussion about interactions and/or allowed final states. Since the photon is the lowest energy state (of a photon?) it cannot decay into something. And while it doesnt meet any interacting (virtual or other) particle, there is no reason for any transformation.