As you know, Space X streams its missions and the speed and altitude data of the vehicle is shown. After stage separation, stage one gains speed and accelerates in its decent trajectory till reentry engine burn. With its engine on, it is obvious that the vehicle decelerates, but after engine burn out, it still loses speed and decelerates until the landing burn. Why does this happen? I expected the vehicle to accelerate after reentry burn out due to gravity.
The falcon 9 decelerates because of the air friction. One example is when you jump out of a plane you continue to accelerate until you reach a speed of around 240 km/h. The higher the air density is the slower you will get. With the Falcon 9 rocket it will turn on it engines to avoid burning up because of the high air friction, then it will slow down using aerodynamic drag.
In two words, air resistance. While the Falcon 9 is coming down, it is constantly "shoving" air particles out of the way. The air particles don't "want" to move, and before they will do so they slow down the vehicle by a tiny bit. Doing this also make friction, which then turns itself to heat. The entry burn is only to avoid being lit on fire by the heat caused by the friction. Of course, the obvious question is, why isn't is already slowing down before that. Well, the further down you get in the atmosphere, the denser that the air is, and therefore there are more air particles. That causes more air particles to have to move, causing a larger deceleration. Since prior to the entry burn it is higher up, the downward pulling force of gravity is stronger than the stopping force of air resistance.