The pressure typically peaks very early in bullet travel and drops off as the bullet moves down the bore. This is because the volume of space behind the bullet grows as the bullet moves down the bore and the gas has more space to fill. More space to fill with the same volume of gas means less pressure.
The fact that the pressure is usually dropping by the time the bullet has moved a significant distance down the bore doesn't mean that the bullet stops accelerating. As long as the force on the back of the bullet due to pressure is greater than combined force of friction from the bore and the force against the front of the bullet from pushing the air in the bore out of the way, the bullet will continue to accelerate.
This also means that even after all the powder has been consumed, the bullet can still be accelerating as long as the force applied to the back of the bullet by the gas pressure exceeds the combined forces retarding the bullet's movement.
Force pushing bullet > Force retarding bullet--acceleration
Force pushing bullet = Force retarding bullet--constant velocity
Force pushing bullet < Force retarding bullet--deceleration
Yes. Bullets can start to slow down in the bore, but it's not common with normal barrel lengths. Even with the pressure starting to drop off almost as soon as the bullet starts moving and continuing to drop as the bullet moves down the bore, there's still usually enough force maintained all the way down the bore to keep accelerating the bullet until it exits the bore and the gas escapes. That's because although the pressure is decreasing as the bullet moves down the bore, it starts off at a very high level. So even though it is decreasing, the amount of force it applies is still very large and remains larger than the combined retarding forces all the way down the bore.
If I'm pushing on a block from one side with a force of 10 units and the resistance totals to a force of 1 unit, then the block will accelerate. Let's say that as soon as it starts moving, I start reducing the amount of force I'm pushing with by 1 unit per second. After 5 seconds, I'm now only pushing with 5 units. So the amount of force I'm pushing with has decreased, but because I'm still pushing with more force than the resistance force of 1 unit, the block is still accelerating. It's still building speed even though I've reduced how much force I'm applying.
The block will continue building speed (the speed increases will be smaller as time goes on since the force I'm pushing with will get smaller over time and as the force imbalance gets smaller, the amount of acceleration reduces) until we get to 9 seconds. At that point, the force I'm pushing with (1 unit--> 10 units - 1 unit per second for 9 seconds) is equal to the force that is resisting the block. Let's say when I detect that moment, I stop decreasing my force and continue pushing with a constant force of 1 unit. Now, since the forces equal, the acceleration will stop--no more speed will be added. It won't slow down, but it will stop speeding up.
If I reduce my pushing force further, now the resistance force of 1 unit is greater than the force I'm pushing with and the block will actually start to slow down.
So, the issue isn't whether the pressure is increasing or decreasing, the issue is whether the pressure is pushing on the back of the bullet with more force than the combined forces that are trying to slow the bullet down. Whether the pressure is increasing or decreasing, the bullet will accelerate as long as the force on the back is greater than the combined slowing forces. Whether the pressure is increasing or decreasing, the bullet will slow down if the force on the back of the bullet is less than the combined slowing forces.
