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 its 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 makes a lot of heat. Actually, the only purpose of the entry burn is only to avoid being lit on fire by the heat. If heat wasn't an issue, then SpaceX would skip the entry burn as it will slow down aerodynamically (which takes no propellent). The entry burn is done because it will overheat before slowing down enough. 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, more air particles pushing back, and more 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. One last thing to note is that on most launches, rocket actually continues accelerating for a bit after the entry burn and then starts decelerating again. This is because it is too high or going to slow (or a combination of the two) at entry burn shutdown on certain missions and therefore doesn't have enough drag to slow it down yet.