Problem with closing high side P mosfet using B type amplifier
The problem seems to lay with the negative feedback the gate of the MOSFET is generating when it is being turned off.
During the ON phase, everything works as expected.
Operation: The FET \$Q_1\$ is turned on, then the PNP is turned on, and the gate of the PFET is pulled to ground.
During the OFF phase, the PFET is not fully turned off.
Operation: The FET \$Q_1\$ is turned off, then the NPN is turned on. The gate of the PFET starts to be charged and consequently its voltage increases. As its voltage increases it generates a negative feedback, thus the voltage across the base resistor \$R_1\$ starts to reduce and so does the biasing current. This in turn, lets less current to flow to the gate of the PFET through the NPN transistor. Basically you are creating a voltage regulator.
How to fix it
You could flip the BJTs and operate then in a push-pull way, by connecting them both in a common emitter configuration, like the following:

The slew rate of the gate charge can be optimized by changing resistors \$R_1\$ and \$R_4\$.