Proton beam transport in the context of proton driven Fast Ignition is usually assumed to be stable due to protons high inertia, but an analytical analysis of the process is still lacking. The stability of a charge and current neutralized proton beam passing through a plasma is therefore conducted here, for typical proton driven Fast Ignition parameters. In the cold regime, two fast growing Buneman-like modes are found, with an inverse growth-rate much smaller than the beam time-of-flight to the target core. The stability issue is thus not so obvious, and Kinetic effects are investigated. One unstable mode is found stabilized by the background plasma protons and electrons temperatures. The second mode is also damped, providing the proton beam thermal spread is larger than $\sim$ 10 keV. In Fusion conditions, the beam propagation should therefore be stable.